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151 results on '"García-Delgado, R."'

1. Homogeneous quadratic Lie super algebras

Author

García-Delgado, R.

Subjects
Mathematics - Rings and Algebras, 17Bxx, 17B05, 17B60, (Primary) 15A63, 17B30 (Secondary)
Abstract

In this work we state a version of the double extension for homogeneous quadratic Lie super algebras that includes even and odd cases. We prove that any indecomposable, non-simple and homogeneous quadratic Lie super algebra is obtained by means of this type of double extension. We also show that with this construction we can recover previously studied cases as well as some other which can not be recover with former versions of double extensions.

Published
2024

2. Invariant Metrics on Nilpotent Lie algebras

Author

García-Delgado, R.

Subjects
Mathematics - Rings and Algebras, 17B30 17B05 15A63 (Primary), 17B56 17B20 (Secondary)
Abstract

We state criteria for a nilpotent Lie algebra $\g$ to admit an invariant metric. We use that $\g$ possesses two canonical abelian ideals $\ide(\g) \subset \mathfrak{J}(\g)$ to decompose the underlying vector space of $\g$ and then we state sufficient conditions for $\g$ to admit an invariant metric. The properties of the ideal $\mathfrak{J}(\g)$ allows to prove that if a current Lie algebra $\g \otimes \Sa$ admits an invariant metric, then there must be an invariant and non-degenerate bilinear map from $\Sa \times \Sa$ into the space of centroids of $\g/\mathfrak{J}(\g)$. We also prove that in any nilpotent Lie algebra $\g$ there exists a non-zero, symmetric and invariant bilinear form. This bilinear form allows to reconstruct $\g$ by means of an algebra with unit. We prove that this algebra is simple if and only if the bilinear form is an invariant metric on $\g$.

Published
2024

3. Inductive description of quadratic Hom-Lie algebras with twist maps in the centroid

Author

García-Delgado, R.

Subjects
Mathematics - Rings and Algebras, 17B61, 17A30 (Primary) 17B60, 17D30 (Secondary)
Abstract

In this work we give an inductive way to construct quadratic Hom-Lie algebras with twist maps in the centroid. We focus on those Hom-Lie algebras that are not Lie algebras. We prove that the twist map of a Hom-Lie algebra of this type must be nilpotent and the Hom-Lie algebra has trivial center. We also prove that there exists a maximal ideal containing the kernel and the image of the twist map. Then we state an inductive way to construct this type of Hom-Lie algebras -- similar to the double extension procedure for Lie algebras -- and prove that any indecomposable quadratic Hom-Lie algebra with nilpotent twist map in the centroid, which is not a Lie algebra, can be constructed using this type of double extension.

Published
2024

4. On Cohomology group of current Lie algebras

Author

García-Delgado, R.

Subjects
Mathematics - Rings and Algebras, 17B05, 17B56, 17B60 (Primary) 17B10, 17B20 (Secondary)
Abstract

In this work we state a result that relates the cohomology groups of a Lie algebra $\mathfrak{g}$ and a current Lie algebra $\mathfrak{g} \otimes \mathcal{S}$, by means of a short exact sequence -- similar to the universal coefficients theorem for modules -- where $\mathcal{S}$ is a finite dimensional, commutative and associative algebra with unit over a field $\mathbb{F}$. Although this result can be applied to any Lie algebra, we determine the cohomology group of $\mathfrak{g} \otimes \mathcal{S}$, where $\mathfrak{g}$ is a semisimple Lie algebra.

Published
2023

5. Double extensions for quadratic Hom-Lie algebras with equivariant twist maps

Author

García-Delgado, R., Salgado, G., and Sánchez-Valenzuela, O. A.

Subjects
Mathematics - Rings and Algebras, 17B61, 17B30 (Primary) 17A30, 17B60, 17D30 (Secondary)
Abstract

Quadratic Hom-Lie algebras with equivariant twist maps are studied. They are completely characterized in terms of a maximal proper ideal that contains the kernel of the twist map and a complementary subspace to it that is either 1-dimensional, or has the structure of a simple Lie algebra. It is shown how the analogue of the double extension construction works well for quadratic Hom-Lie algebras with equivariant twist maps and prove that any indecomposable and quadratic Hom-Lie algebra with equivariant and nilpotent twist map can be identified with such a double extension., Comment: Theorem A, page 19, is wrong. The only simple Lie algebra for which the statement of the theorem is valid is the simple Lie algebra of rank one

Published
2023

6. On quadratic Hom-Lie algebras with twist maps in their centroids and their relationship with quadratic Lie algebras

Author

García-Delgado, R., Salgado, G., and Sánchez-Valenzuela, O. A.

Subjects
Mathematics - Rings and Algebras, 17Bxx, 17B60 (Primary) 17B20, 17B30, 17B40 (Secondary)
Abstract

Hom-Lie algebras having non-invertible twist maps in their centroids are studied. Central extensions of Hom-Lie algebras having these properties are obtained and shown how the same properties are preserved. Conditions are given so that the produced central extension has an invariant metric with respect to its Hom-Lie product making its twist map self-adjoint when the original Hom-Lie algebra has such a metric. This work is focused on algebras with these properties and following Benayadi and Makhloufwe call them quadratic Hom-Lie algebras. It is shown how a quadratic Hom-Lie algebra gives rise to a quadratic Lie algebra and that the Lie algebra associated to the given Hom-Lie central extension is a Lie algebra central extension of it. It is also shown that if the Hom-Lie product is not a Lie product, there exists a non-abelian algebra, which is in general non-associative too, the commutator of whose product is precisely the Hom-Lie product of the Hom-Lie central extension. Moreover, the algebra whose commutator realizes this Hom-Lie product is shown to be simple if the associated Lie algebra is nilpotent. Non-trivial examples are provided.

Published
2022

7. Invariant metrics on current Lie algebras

Author

García-Delgado, R.

Subjects
Mathematics - Rings and Algebras, Primary: 17A45, 17B05, 17B56 Secondary: 15A63, 17B60
Abstract

In this work we state conditions for a current Lie algebra $\g \otimes \mathcal{S}$ to admit an invariant metric, where $\g$ is a quadratic Lie algebra and $\mathcal{S}$ is an associative and commutative algebra with unit. We also consider the reciprocal: if $\g \otimes \mathcal{S}$ admits an invariant metric, we state necessary and sufficient conditions for $\g$ to admit an invariant metric. In particular, we show that if $\g$ is an indecomposable quadratic Lie algebra, then $\g \otimes \mathcal{S}$ admits an invariant metric if and only if $\mathcal{S}$ also admits an invariant, symmetric and non-degenerate bilinear form. In addition, we prove a theorem similar to the double extension for $\g \otimes \mathcal{S}$, where $\g$ is an indecomposable, nilpotent and quadratic Lie algebra.

Published
2022

9. Hom-Lie algebra structures on quadratic Lie algebras and twisted invariant Killing-like forms defined on them

Author

García-Delgado, R., Salgado, G., and Sánchez-Valenzuela, O. A.

Subjects
Mathematics - Rings and Algebras, Primary:17Bxx, 17B60. Secondary: 17B20, 17B30, 17B40
Abstract

Hom-Lie algebras defined on central extensions of a given quadratic Lie algebra that in turn admit an invariant metric, are studied. It is shown how some of these algebras are naturally equipped with other symmetric, bilinear forms that satisfy an invariant condition for their twisted multiplication maps. The twisted invariant bilinear forms so obtained resemble the Cartan-Killing forms defined on ordinary Lie algebras. This fact allows one to reproduce on the Hom-Lie algebras hereby studied, some results that are classically associated to the ordinary Cartan-Killing form.

Published
2020

10. Covariant functors commuting with direct limits

Author

García-Delgado, R.

Subjects
Mathematics - Category Theory, Mathematics - Representation Theory, Primary:18Axx Secondary: 18A30
Abstract

In this work we state conditions on a covariant right exact functor so that it commutes with direct limits. These conditions are related to the commutativity of the functor under direct limits of projective modules. We prove that if the functor commutes with direct limits of projective modules, then the functor commutes with direct limits.

Published
2020

11. On Solvable Quadratic Lie algebras having an Abelian descending central ideal

Author

García-Delgado, R., Salgado, G., and Sánchez-Valenzuela, O. A.

Subjects
Mathematics - Rings and Algebras, Primary:17A45, 17B05, 17B56. Secondary: 15A63, 17B30, 17B40
Abstract

Solvable Lie algebras having at least one Abelian descending central ideal are studied. It is shown that all such Lie algebras can be built up from canonically defined ideals. The nature of such ideals is elucidated and their construction is provided in detail. An approach to study and to classify these Lie algebras is given through the theory of extensions via appropriate cocycles and representations on which a group action is naturally defined. Also, necessary and sufficient conditions for the existence of invariant metrics on the studied extensions are given. It is shown that any solvable quadratic Lie algebra $\g$ having an Abelian descending central ideal is of the form $\g=\h\oplus\a\oplus\h^*$, where $\h^*\simeq \ide(\g)$ and $\a \oplus \h^{*}\simeq \j(\g)$ are in fact two canonically defined Abelian ideals of $\g$ satisfying $\ide(\g)^\perp=\j(\g)$. As an example, a classification of this type of quadratic Lie algebras is given assuming that $\j(\g)/\ide(\g)$ is an $r$-dimensional vector space and $\g/\j(\g)$ is the 3-dimensional Heisenberg Lie algebra., Comment: This is a revised version of the manuscript On Quadratic Lie Algebras With Non-trivial Center [arXiv:1911.05009v3]. We submitted it for publication and the reviewer found a mistake in Lemma 2.6. The problem does not appear for Lie algebras with one Abelian descending central ideal. Thus, we ended up with this manuscript in whose title we have included the additional hypothesis

Published
2019

12. Generalized derivations and Hom-Lie algebra structures on $\mathfrak{sl}_2$

Author

García-Delgado, R.

Subjects
Mathematics - Rings and Algebras, Primary: 17B05, 17B20, 17B40. Secondary: 17B60, 17B10
Abstract

The purpose of this paper is to show that there are Hom-Lie algebra structures on $\mathfrak{sl}_2(\mathbb{F}) \oplus \mathbb{F}D$, where $D$ is a special type of generalized derivation of $\mathfrak{sl}_2(\mathbb{F})$, and $\mathbb{F}$ is an algebraically closed field of characteristic zero. It is shown that the generalized derivations $D$ of $\mathfrak{sl}_2(\mathbb{F})$ that we study in this work, satisfy the Hom-Lie Jacobi identity for the Lie bracket of $\mathfrak{sl}_2(\mathbb{F})$. We study the representation theory of Hom-Lie algebras within the appropriate category and prove that any finite dimensional representation of a Hom-Lie algebra of the form $\mathfrak{sl}_2(\mathbb{F}) \oplus \mathbb{F}D$, is completely reducible, in analogy to the well known Theorem of Weyl from the classical Lie theory. We apply this result to characterize the non-solvable Lie algebras having an invertible generalized derivation of the type of $D$. Finally, using root space decomposition techniques we provide an intrinsic proof of the fact that $\mathfrak{sl}_2(\mathbb{F})$ is the only simple Lie algebra admitting non-trivial Hom-Lie structures.

Published
2019

13. On 3-dimensional complex Hom-Lie algebras

Author

García-Delgado, R., Salgado, G., and Sánchez-Valenzuela, O. A.

Subjects
Mathematics - Rings and Algebras, Primary: 17-XX, Secondary: 17A30, 17A36, 17BXX, 17B60
Abstract

We study and classify the 3-dimensional Hom-Lie algebras over $\mathbb{C}$. We provide first a complete set of representatives for the isomorphism classes of skew-symmetric bilinear products defined on a 3-dimensional complex vector space $\mathfrak{g}$. The well known Lie brackets for the 3-dimensional Lie algebras are included into appropriate isomorphism classes of such products representatives. For each product representative, we provide a complete set of canonical forms for the linear maps $\mathfrak{g} \to \mathfrak{g}$ that turn $g$ into a Hom-Lie algebra, thus characterizing the corresponding isomorphism classes. As by-products, Hom-Lie algebras for which the linear maps $\mathfrak{g} \to \mathfrak{g}$ are not homomorphisms for their products, are exhibited. Examples also arise of non-isomorphic families of HomLie algebras which share, however, a fixed Lie-algebra product on $\mathfrak{g}$. In particular, this is the case for the complex simple Lie algebra $\mathfrak{sl}_2(\mathbb{C})$. Similarly, there are isomorphism classes for which their skew-symmetric bilinear products can never be Lie algebra brackets on $\mathfrak{g}$.

Published
2019

14. Invariant metrics on central extensions of Quadratic Lie algebras

Author

García-Delgado, R., Salgado, G., and Sánchez-Valenzuela, O. A.

Subjects
Mathematics - Rings and Algebras, 17Bxx, 17B05, 17B60 (Primary), 15A63, 17B30 (Secondary)
Abstract

A quadratic Lie algebra is a Lie algebra endowed with a symmetric, invariant and non degenerate bilinear form; such a bilinear form is called an invariant metric. The aim of this work is to describe the general structure of those central extensions of quadratic Lie algebras which in turn have invariantmetrics. The structure is such that the central extensions can be described algebraically in terms of the original quadratic Lie algebra, and geometrically in terms of the direct sum decompositions that the invariant metrics involvedgive rise to.

Published
2018

19. Invariant metrics on current Lie algebras.

Author

García-Delgado, R.

Subjects
*LIE algebras, *COMMUTATIVE algebra, *ASSOCIATIVE algebras, *INDECOMPOSABLE modules
Abstract

In this work we state conditions for a current Lie algebra g ⊗ S to admit an invariant metric, where g is a quadratic Lie algebra and S is an associative and commutative algebra with unit. We show that if g is an indecomposable quadratic Lie algebra, then g ⊗ S admits an invariant metric if and only if S also admits an invariant metric. In addition, we prove a theorem similar to the double extension for g ⊗ S , where g is an indecomposable, nilpotent and quadratic Lie algebra. [ABSTRACT FROM AUTHOR]

Published
2023
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23. Generalized derivations and Hom-Lie algebra structures on sl2.

Author

García-Delgado, R.

Subjects
REPRESENTATION theory, LIE algebras, ALGEBRA, REPRESENTATIONS of algebras
Abstract

The purpose of this paper is to show that there are Hom-Lie algebra structures on s l 2 (F) ⊕ F D , where D is a special type of generalized derivation of s l 2 (F) , and F is an algebraically closed field of characteristic zero. We study the representation theory of Hom-Lie algebras within the appropriate category and prove that any finite dimensional representation of a Hom-Lie algebra of the form s l 2 (F) ⊕ F D is completely reducible, analogously to the well-known theorem of Weyl from the classical Lie theory. We apply this result to characterize the non-solvable Lie algebras of this type having an invertible generalized derivation D. [ABSTRACT FROM AUTHOR]

Published
2022
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27. Abstracts

Author

Derlon J. M., Petit-taboué M. C., Dauphin F., Courtheoux P., Chapon F., Creissard P., Darcel F., Houtteville J. P., Kaschten, B., Sadzot, B., Stevenaert, A., Tjuvajev, Juri G., Macapinlac, Homer A., Daghighian, Farhad, Ginos, James Z., Finn, Ronald D., Jiaju Zhang, M. S., Beattie, Bradley, Graham, Martin, Larson, Steven M., Blasberg, Ronald G., Levivier, M., Goldman, S., Pirotte, B., Brucher, J. M., Balériaux, D., Luxen, A., Hildebrand, J., Brotchi, J., Go K. G., Kamman R. L., Mooyaart E. L., Heesters M. A. A. M., Sijens, P. E., Oudksrk, M., van Dijk, P., Levendag, P. C., Vecht, Ch. J., Metz, R. J., Kennedy, D. N., Rosen, B. R., Hochberg, F. H., Fishman, A. J., Filipek, P. A., Caviness, V. S., Gross, M. W., Weinzierl, F. X., Trappe, A. E., Goebel, W. E., Frank, A. M., Becker, Georg, Krone, Andreas, Schmidt, Karsten, Hofmann, Erich, Bogdahn, Ulrich, Bencsch, H., Fclber, S., Finkenstedt, G., Kremser, C., Sfockhammer, G., Aichner, F., Bogdahn U., Fröhlich T., Becker G., Krone A., Schlief R., Schürmann J., Jachimczak P., Hofmann E., Roggendorf W., Roosen K., Carapella, C. M., Carpinelli, G., Passalacqua, R., Raus, L., Giannini, M., Mastrostefano, R., Podo, F., Tofani, A., Maslrostefano, R., Mottoles, M., Ferraironi, A., Scelsa, M. G., Oppido, P., Riccio, A., Maini, C. L., Collombier, L., Taillandier, L., Dcbouverie, M., Laurens, M. H., Thouvenot, P., Weber, M., Bertrand, A., Cruickshank G. S., Patterson J., Hadley D., De Witte, Olivier, Hildebrand, Jerzy, Luxen, André, Goldman, Serge, Ernestus, R. -I., Bockhorst, K., Eis, M., Els, T., Hoehn-Berlage, M., Gliese, M., Fründ, R., Geissler, A., Woertgen, C., Holzschuh, M., Goldman, Serge, Levivier, M., Pirotte, B., Brucher, J. M., Luxen, A., Brotchi, J., Hildebrand, J., Hausmann, O., Merlo, A., Jerrnann, E., Uirich, J., Chiquet-Ehrismann, R., Müller, J., Mäcke, H., Gratzl, O., Herholz, K., Ghaemi, M., Würker, M., Pietrzyk, U., Heiss, W. -D., Kotitschke, K., Brandl, M., Tonn, J. C., Haase, A., Bogdahn, U., Kotitschke, K., Muigg, S., Felber, S., Aichner, F., Haase, A., Bogdahn, U., Krone A., Becker G., Woydt M., Roggendorf W., Hofmann E., Bogdahn U., Roosen K., Lanfermann, Heinrich, Heindel, Walter, Kugel, Harald, Erneslus, Ralf -Ingo, Röhn, Gabricle, Lackner, Klaus, Metz, R. J., Kennedy, D. N., Pardo, F. S., Kutke, S., Sorensen, A. G., Hochberg, F. H., Fishman, A. J., Filipek, P. A., Rosen, B. R., Caviness, V. S., Mechtler, L. L., Withiam-Lench, S., Shin, K., Klnkel, W. R., Patel, M., Truax, B., Kinkel, P., Shin, K., Mechtler, L., Ricci M., Pantano P., Maleci A., Pierallini S., Di Stefano D., Bozzao L., Cantore G. P., Röhn, Gabriele, Els, T., Schröder, R., Hoehn-Berlage, M., Ernestus, R. -I., Ruda, R., Mocellini, C., Soffietti, R., Campana, M., Ropolo, R., Riva, A., de Filippi, P. G., Schiffer, D., Salgado D., Rodrigues M., Salgado L., Fonseca A. T., Vieira M. R., Bravo Marques J. M., Satoh, H., Uozumi, T., Kiya, K., Kurisu, K., Arita, K., Sumida, M., Ikawa, F., Tzuk-Shina, Tz., Gomori, J. M., Rubinstein, R., Lossos, A., Siegal, T., Vaalburg, W., Paans, A. M. J., Willemsen, A. T. M., van Waarde, A., Pruim, J., Visser, G. M., Go, K. G., Valentini, S., Ting, Y. L. T., De Rose, R., Chidichimo, G., Corricro, G., van Lcycn-Pilgram, Karin, Erncslus, Ralf -Ingo, Klug, Norfried, van Leyen-Pilgram, K., Ernestus, R. -I., Schröder, R., Klug, N., Woydt M., Krone A., Tonn J. C., Becker G., Neumann U., Roggendorf W., Roosen K., Plate, Karl H., Breier, Georg, Millaucr, Birgit, Weich, Herbert A., Ullrich, Axel, Risau, Werner, Roosen N., Chopra R. K., Mikkelsen T., Rosenblum S. D., Yan P. S., Knight R., Windham J., Rosenblum M. L., Schiffer, D., Attanasio, A., Cavalla, P., Chio, A., Giordana, M. T., Migheli, A., Amberger, V., Hensel, T., Schwab, M. E., Cervoni, Luigi, Celli, Paolo, Tarantino, Roberto, Huettner, C., Tonn, J. C., Berweiler, U., Roggendorf, W., Salmon, I., Rorive, S., Rombaut, K., Pirotte, B., Haot, J., Brotchi, J., Kiss, R., Maugard-Louboutin C., Charrier J., Fayet G., Sagan C., Cuillioere P., Ricolleau G., Martin S., Menegalli-Bogeelli D., Lajat Y., Resche F., Molnàr, Péter, Bárdos, Helga, Ádány, Róza, Rogers, J. P., Pilkington, G. J., Pollo, B., Giaccone, G., Allegranza, A., Bugiani, O., Prim, J., Badia, J., Ribas, E., Coello, F., Shezen, E., Lossos, A., Abramsky, O., Siegal, T., Scerrati M., Roselli R., Iacoangeli M., Pompucci A., Rossi G. F., Deeb, Saleh M. Al., Koreich, Osama, Yaqub, Basim, Moutaery, Khalaf R. Al., Giordana, M. T., Cavalla, P., Chio, A., Marino, S., Vigliani, M. C., Schiffer, D., Deburghgraeve, V., Darcel, F., Gedouin, D., Hassel, M. Ben, Guegan, Y., Jeremic, B., Grujicic, D., Antunovic, V., Matovic, M., Shibamoto, Y., Kallio, Merja, Huhmar, Helena, Kudoh, Ch., Detta, A., Sugiura, K., Hitchcock, E. R., Mastrostefano, R., Di Russo, R., Cipriani§, M., Occhipinti, E. M., Conti, E. M. S., Clowegeser A., Ortler M., Seiwald M., Kostron H., Rajan B., Ross G., Lim C., Ashlcy S., Goode D., Traish D., Brada M., Sanden, G. A. C. vd, Schouten, L. J., Coebergh, J. W. W., Razenberg, P. P. A., Twijnstra, A., Snilders-Keilholz, A., Voormolen, J. H. C., Hermans, J., Leer, J. W. H., Taillandier, L., Baylac, F., Dcbouvcrie, M., Anxionnal, R., Bracard, S., Vignand, J. M., Duprcz, A., Weber, M., Winking, M., Böker, D. K., Simmet, T., Rothbart, David, Strugar, John, Balledux, Jeroen, Criscuolo, Gregory R., Jachimczak, Piotr, Blesch, Armin, Heβdörfer, Birgit, Bogdahn, Ulrich, Ernestus, Ralf -Ingo, Schröder, Roland, Klug, Norfrid, Krouwer, H. G. J., Duinen, S. G. v., Algra, A., Zentner, J., Wolf, H. K., Ostertun, B., Hufnagel, A., Campos, M. G., Solymosi, L., Schramm, J., Newlands, E. S., O'Reilly, S. M., Brampton, M., Soffietti, R., Chio, A., Mocellini, C., Ruda, R., Vigliani, M. C., Schiffer, D., Sciolla, R., Seliak, D., Henriksson, R., Bergenheim, A. T., Björk, P., Gunnarsson, P. -O., Hariz, Ml., Grant, R., Collie, D., Gregor A., Ebmeier K. P., Jarvis G., Lander F., Cull A., Sellar R., Brada, M., Thomas, C., Elyan, S., Hines, F., Ashley, S., Stenning, S., Bernstein J. J., Goldberg W. J., Roelcke U., Von Ammon K., Hausmann O., Radu E. W., Kaech D., Leenders K. L., Fitzek, II, M. M., Aronen J. Efird, Hochberg, F., Gruber, M., Schmidt, E., Rosen, B., Flschman, A., Pardo, P., Afra U. M. U., Sipos, L., Slouik, F., Boiardi A., Salmaggi A., Pozzi A., Farinotti L., Fariselli L., Silvani A., Brandes, A., Scelzi, E., Rigon, A., Zampieri, P., Pignataro, M., Amanzo, P. D'., Amista, P., Rotilio, A., Fiorentino, M. V., Thomas, R., Brazil, L., O'Connor, A. M., Ashley, S., Brada, M., Salvati, Maurizio, Cervoni, Luigi, Puzzilli, Fabrizio, Cervoni, Luigi, Salvati, Maurizio, Raguso, Michele, Cruickshank G. S., Duckworth R., Rumpling R., Rottuci M., Fariselli L., Boiardi A., Broggi G., Plrint, N. G., Sabattini, E., Manetto, V., Gambacorta, H., Poggi, S., Pileri, S., Ferracini, R., Grant, R., Plev D. V., Hopf N. J., Knosp E., Bohl J., Perncczky A., Kiss, R., Salmon, I., Catnby, I., Dewitte, O., Brotchi, J., Pasteels, J. L., Camby, I., Salmon, I., Darro, F., Danguy, A., Brotchi, J., Pasteels, J. L., Kiss, R., Kiu, M. C., Lai, G. M., Yang, T. S., Ng, K. T., Chen, J. S., Chang, C. N., Leung, W. M., Ho, Y. S., Rychter, M. Deblec, Klimek, A., Liberski, P. P., Karpinaka, A., Krauseneck P., Schöffel V., Müller B., Kreth, F. W., Faist, M., Warnke, P. C., Ostertag, C. B., Nielen, K. M. B. v., Visscr, M. C., Lebrun C., Lonjon M., Desjardin T., Michiels J. F., Chanalet Sa. Lagrange J. L., Roche J. L., Chatel M., Mastronardi L., Puzzilli F., Osman Farah J., Lunardi P., Matsutani, M., Ushio, Y., Takakura, K., Menten, Johan, Hamers, Han, Ribot, Jacques, Dom, René, Tcepen, Hans, Müller B., Weidner N., Krauseneck P., Naujocks, G., van Roost, D., Wiestler, O. D., Kuncz, A., Nieder, C., Setzel-Sesterhein, M., Niewald, M., Schnabel, I., O'Neill, K. S., Kitchen, N. D., Wilkins, P. R., Marsh, H. T., Pierce, E., Doshi, R., Deane, R., Previtali, S., Quattrini, A., Nemni, R., Ducati, A., Wrabetz, L., Canal, N., Punt, C. J. A., Stamatakis, L., Giroux, B., Rutten, E., Quigley, Matthew R., Beth Sargent P. A. -C., Flores, Nicholas, Simon, Sheryl, Maroon, Joseph C., Quigley, Matthew R., Beth Sargent P. A. -C., Flores, Nicholas, Maroon, Joseph C., Rocca A. A., Gervasoni C., Castagna A., Picozzi P., Giugni E., Rocca A. A., Tonnarelli G. P., Ducati A., Mangili F., Truci G., Canal N., Giovanelli M., Roelcke U., Von Ammon K., Radu E. W., Leenders K. L., Sachsenheimer, W., Bimmler, T., Seiwald M., Eiter H. Rhomberg W., Ortler M., Obwegesser A., Kostron H., Steilen H., Henn W., Moringlane J. R., Kolles H., Feiden W., Zang K. D., Sleudel W. I., Steinbrecher, Andreas, Schabet, Martin, Heb, Clemens, Bamberg, Michael, Dichgans, Johannes, Stragliotto, G., Delattre, J. Y., Poisson, M., Zampieri, P., Brandes, A., Rigon, A., Tosatto, L., D'Amanzo, P., Menicucci, N., Rotilio, A., Mingrino, S., Steudel, W. I., Feld, R., Henn, W., Zang, K. D., Maire, J. Ph., Caudry, M., Guerin, J., Celerier, D., Salem, N., Demeaux, H., Fahregat, J. F., Kusak, M. E., Bucno, A., Albisua, J., Jerez, P., Sarasa, J. L., Garefa, R., de Campos, J. M., Kusak, M. E., de Campos, J. M., Bueno, A., García-Delgado, R., Sarasa, J. L., García-Sola, R., Lantsov A. A., Shustova T. I., Lcnartz, D., Wellenreuther, R., von Deirnling, A., Köning, W., Menzel, J., Scarpa, S., Manna, A., Reale, M. G., Oppido, P. A., Carapella, C. M., Frati, L., Valery, C. A., Ichen, M., Foncin, J. P., Soubrane, C., Khayat, D., Philippon, J., Vaz, R., Cruz, C., Weis S., Protopapa D., März R., Winkler P. A., Reulen H. J., Bise K., Beuls E., Berg J., Deinsberger, W., Böker, D. K., Samii, M., Caudry, M., Darrouzet, V., Guérin, J., Trouette, R., Causse, N., Bébéar, J. P., Parker, F., Vallee, J. N., Carlier, R., Zerah, M., Lacroix-Jousselin, C., Piepmeier, Joseph M., Kveton, John, Czibulka, Agnes, Tigliev G. S., Chernov M. P., Maslova L. N., Valdueza, José M., Jänisch, Werner, Bock, Alexander, Harms, Lutz, Bessell, E. M., Graus, F., Punt, J., Firth, J., Hope, T., Koriech, Osama, Al Deeb, Saleh, Al Moutaery, Khalaf, Yaqub, B., Silvani A., Salmaggi A., Pozzi A., Franzini A., Boiardi A., Goldbrunner, R., Warmuth-Metz, M., Paulus, W., Tonn, J. -Ch., Roosen, K., Strik I. I., Müller B., Markert C., Pflughaupt K. -W., Krauseneck P., O'Neill, B. P., Dinapoli, R. P., Voges, J., Sturm, V., Deuß, U., Traud, C., Treuer, H., Lehrke, R., Kim, D. G., Müller, R. P., Alexandrov Yu. S., Moutaery, K., Aabed, M., Koreich, O., Ross, G. M., Rajan, B., Traish, D., Ashley, S., Ford, D., Brada, M., Schmeets, I. L. O., Jager, J. J., Pannebakker, M. A. G., de Jong, J. M. A., van Lindert, E., Knosp, E., Kitz, K., Blond, S., Dubois, F., Assaker, R., Baranzelli, M. C., Sleiman, M., Pruvo, J. P., Coche-Dequeant, B., Matsutani M., Takakura K., Sano K., PetriČ-Grabnar, G., Jereb, B., Župančič, N., Koršič, M., Rainov N. G., Burkert W., Ushio, Yukitaka, Kochi, Masato, Itoyama, Youichi, de Campos, J. M., Kusak, M. E., Sarasa, J. L., García, R., Bueno, A., Ferrando, L., Hoang-Xuan, K., Sanson, M., Merel, P., Delattre, J. Y., Poisson, M., Delattre, O., Thomas, G., Hoang-Xuan, K., Delattre, J. Y., Poisson, M., Thomas, G., Haritz, D., Obersen, B., Grochulla, F., Gabel, D., Haselsberger K., Radner H., Pendl G., Brada, M., Laing, R. W., Warrington, A. P., Nowak, P. J. C. M., Kolkman-Deurloo, I. K. K., Visser, A. G., Berge, Hv. d., Niël, C. G. J. H., Levendag, P. C., Bergström P., Hariz M., Löfroth P. -O., Bergenheim T., Henriksson R., Blond, S., Assaker, R., Cortet-rudelli, C., Dewailly, D., Coche-dequeant, B., Castelain, B., Dinapoli, R., Shaw, E., Coffey, R., Earle, J., Foote, R., Schomberg, P., Gorman, D., Girard N., Courel M. N., Delpech B., Haselsberger K., Friehs G. M., Schröttner O., Pendl G., Pötter, R., hawliczek, R., Sperveslage, P., Prott, F. J., Wachter, S., Dieckmann, K., Würker, M., Herholz, K., Pietrzyk, U., Voges, J., Treuer, H., Sturm, V., Bauer, B., Heiss, W. -D., Jund, R., Zimmermann, F., Feldmann, H. J., Gross, M. W., Kneschaurek, P., Molls, M., Lederman, G., Lowry, J., Wertheim, S., Voulsinas, L., Fine, M., Lederman, G., Lowry, J., Wertheim, S., Fine, M., Voutsinas, I., Qian, G., Rashid, H., Lederman, G., Lowry, J., Wertheim, S., Fine, M., Voulsinas, L., Qian, G., Rashid, H., Moutaery, K., Aabed, M., Koreich, O., Scerrati M., Montemaggi P., Iacoangeli M., Pompucci A., Roselli R., Trignani R., Rossi G. F., Shin, K., Mechtler, L., West, C., Grand, W., Shin, K., Sibata, C., West, C., Mechtler, L., Grand, W., Thomas, R., Guerrero, D., James, N., Ashley, S., Gregor, A., Brada, M., Voges, J., Sturm, V., Bramer, R., Pahlke, H., Lehrke, R., Treuer, H., Banik, N., Kim, D. G., Hövels, M., Bernsen H. J. J. A., Rijken P. F. J. W., Van der Sanden B. P. J., Hagemeier N. E. M., Van der Kogel A. J., Koehler P. J., Verbiest H., Jager J., Vecht Ch. J., Ross G. M., McIlwrath A., Brown R., Mottolesb, C., Pierre'Kahn, A., Croux, M., Roche, J. L., Marchai, J., Delhemes, P., Tremoulet, M., Stilhart, B., Chazai, J., Caillaud, P., Ravon, R., Passacha, J., Bouffet, E., Dirven C. M. F., Mooy J. J. A., Molenaar W. M., Lewandowicz, G. M., Grant, N., Harkness, W., Hayward, R., Thomas, D. G. T., Darling, J. L., Delepine, N., Subovici I. I., Cornille B., Markowska S., Alkallaf JC. Desbois, KühI, J., Niethammer, D., Spaar, H. J., Gnekow, A., Havers, W., Berthold, F., Graf, N., Lampert, F., Maass, E., Mertens, R., Schöck, V., Aguzzi, A., Boukhny, A., Smirtukov, S., Prityko, A., Hoiodov, B., Geludkova, O., Nikanorov, A., Levin, P., Rothbart, David, Balledux, Jeroen, Criscuolo, Gregory R., D'haen, B., Van Calenbergh, F., Casaer, P., Dom, R., Menten, J., Goffin, J., Plets, C., Hertel, A., Hernaiz, P., Seipp, C., Siegler, K., Baum, R. P., Maul, F. D., Schwabe, D., Jacobi, G., Kornhuber, B., Hör, G., Menten, J., Casaer, P., Pilkington, G. J., Merzak, A., Rooprai, H. K., Bullock, P., van Domburg P. H. M. F., Wesseling P., Thijssen H. O. M., Wolff, J. E. A., Boos, J., Krähling, K. H., Gressner-Brocks, V., Jürgens, H., Schlegel, J., Scherthan, H., Arens, N., Stumm, Gabi, Kiessling, Marika, Merzak, A., Koochekpour, S., Pilkington, G. J., Reifenberger, G., Reifenberger, J., Liu, L., James, C. D., Wechsler, W., Collins, V. P., Fabel-Schulte, Klaus, Jachimczak, Plotr, Heßdörfer, Birgitt, Baur, Inge, Schlingensiepen, Karl -Hermann, Brysch, Wolgang, Bogdahn, Ulrich, Blesch A., Bosserhoff A. K., Apfel R., Lottspeich F., Jachimczak P., Büttner R., Bogdahn U., Cece, R., Barajon, I., Tazzari, S., Cavaletti, G., Torri-Tarelli, L., Tredici, G., Hecht, B., Turc-Carel, C., Atllas, R., Chatel, M., Gaudray, P., Gioanni, J., Hecht, F., Balledux, Jeroen, Rothbart, David, Criscuolo, Gregory R., de Campos, J. M., Kusak, M. E., Rey, J. A., Bello, M. J., Sarasa, J. L., Dubois, F., Blond, S., Parent, M., Assaker, R., Gosselin, P., Christiaens, J. L., Feld, R., Moringlane, J. R., Steudel, W. I., Schaudies, J. R., Janka M., Tonn J. C., Fischer U., Meese E., Roosen K., Remmelink, M., Salmon, I., Cras, P., Pasteels, J. L., Brotchi, J., Kiss, R., Bensadoun R. J., Frenay M., Formento J. L., Milano G., Lagrange J. L., Grellier P., Lee, J. -Y., Ernestus, R. -I., Riese, H. -H., Cervós-Navarro, J., Reutter, W., Lippitz, B., Scheitinger, C., Scholz, M., Weis, J., Gilsbach, J. M., Füzesi, L., Koochekpour, S., Merzak, A., Pilkington, G. J., Sanson, M., Li, Y. J., Hoang-Xuan, K., Delattre, J. Y., Poisson, M., Hamelin, R., Van de Kelft, Erik, Dams, Erna, Martin, Jean -Jacques, Willems, Patrick, Lehrke R., Voges J., Treuer H., Erdmann J., Müller R. P., Sturm V., Wurm R. E., Warrington A. P., Laing R. W., Sardell S., Hines F., Graham J. D., Brada M., Ushio, Yukitaka, Kuratsu, Jun -ichi, Kochi, Masato, Kitz K., Aichholzer M., Rössler K., Alesch F., Ertl A., Sorensen, P. S., Helweg-Larsen, S., Mourldsen, H., Hansen, H. H., El Sharoum, S. Y., Berfelo, M. W., Theunissen, P. H. M. H., Jager, J. J., de Jong, J. M. A., Fedorcsák, I., Nyáry, I., Osztie, É., Horvath, Á., Kontra, G., Frenay M., Burgoni-chuzel J., Paquis P., Lagrange J. L., Helweg-Larsen, S., Hansen, SW., Sørensen, PS., Salmon, I., Kiss, R., Krauseneck P., Müller B., Morche M., Tonn J. C., Lagerwaard, F. J., Levendag, P. C., Eijkenboom, W. M. H., Schmilz, P. I. M., Lentzsch S., Weber F., Franke J., Dörken B., Lunardi P., Schettini G., Osman Farah J., Qasho R., Mocellini, C., Ruda, R., Soffietti, R., Garabello, D., Sales, S., De Lucchi, R., Vasario, E., Schiffer, D., Muracciole, X., Régis, J., Manera, L., Peragut, J. C., Juin, P., Sedan, R., Nieder, C., Niewald, M., Walter, K., Schnabel, K., Nieder, C., Niewald, N., Nestle, U., Schnabel, K., Berberich, W., Oschmann, P., Theißen R. D., Reuner K. H., Kaps M., Dorndorf W., Martin, K. K., Akinwunmi, J., Rooprai, H. K., Kennedy, A., Linke, A., Ognjenovic, N., Pilkington, G. J., Svadovsky A. I., Peresedov V. V., Bulakov A. A., Butyalko M. Y., Zhirnova I. G., Labunsky D. A., Gnazdizky V. V., Gannushkina I. V., Taphoorn, M. J. B., Potman, R., Barkhof, F., Weerts, J. G., Karim, A. B. M. F., Heimans, J. J., van de Pol, M., van Aalst, V. C., Wilmink, J. T., Twijnstra, A., van der Sande, J. J., Boogerd, W., Kröger, R., Jäger A., Wismeth C., Dekant A., Brysch W., Schlingensiepen K. H., Jachimczak P., Bogdahn U., Pirolte, B., Cool, V., Gérard, C., Levivier, M., Dargent, J. L., Goldman, S., Brotchi, J., Hildebrand, J., Velu, T., Herrlinger, U., Schabet, M., Ohneseit, P., Buchholz, R., Zhu, Jianhong, Reszka, Regina, Weber, Friedrich, Walther, Wolfgang, Zhang, L. I., Brock, Mario, Roosen N., Rock J. P., Zeng H., Feng J., Fenstermacher J. D., Rosenblum M. L., Siegal, T., Gabizon, A., Beljanski M., Crochet S., Bergenheim, A. T., Zackrisson, B., Elfverson, J., Bergström, P., Henriksson, R., Butti, G., Baetta, R., Magrassi, L., De Renzis, M. R., Soma, M. R., Davegna, C., Pezzotta, S., Paoletti, R., Fumagalli, R., Infuso, L., Sankar, A. A., Darling, J. L., Thomas, D. G. T., Defer, G. -L., Brugières, P., Gray, F., Chomienne, C., Poirier, J., Degos, L., Degos, J. D., Colombo, Bruno M., DiDonato, Stefano, Finocchiaro, Gaetano, Hebeda, K. M., Sterenborg, H. J. C. M., Saarnak, A. E., Wolbers, J. G., van Gemert, M. J. C., Kaaijk P., Troost D., Leenstra S., Das P. K., Bosch D. A., Kostron H., Hochleitner B. W., Obwegeser A., Ortler M., Seiwald M., Vooys, W., Krouwer, H. G. J., de Gast, G. C., Marx, J. J. M., Osman Farah J., Lunardi P., Puzzilli F., Menovsky, T., Beek, J. F., Wolbers, J. G., van Gemert, M. J. C., Naujocks, G., Wiestler, O. D., Schirrmacher, V., Schramm, J., Schmitz, A., Eis-Hübinger, A. M., Piepmeier, p. h., Pedersen, Patricia, Greer, Charles, Quigley, Matthew R., Shih, Tommy, Elrifal, Amr, Rothfus, William, Maroon, Joseph C., Rohertson, L., Rampling, R., Whoteley, T. L., Piumb, J. A., Kerr, D. J., Falina, P. A., Crossan, I. M., Roosen N., Rock J. P., Feng J., Zeng H., Ho K. L., Fenstermacher J. D., Rosenblum M. L., Ruchoux, M. M., Vincent, S., Jonca, F., Plouet, J., Lecomte, M., Samid, D., Thibault, A., Ram, Z., Oldfield, E. H., Myers, C. E., Reed, E., Schabet, M., Herrlinger, U., Buchholz, R., Shoshan, Y., Siegal, T., Siegal, T., Shezen, E., Siegal, Tz., Stockhammer, G., Rosenblum, M., Samid, D., Lieberman, F., Terzis, A. J. A., Bjerkvig, R., Laerum, O. D., Arnold, H., Thibault, A., Samid, D., Figg, W. D., Myers, C. E., Reed, E., Thomas, R., Flux, G., Chittenden, S., Doshi, P., Brazil, L., Thomas, D. G. T., Bignor, D., Zalutsky, M., Brada, M., Tjuvajev, Juri, Kaplitt, Michael, Desai, Revathi, Bradley, M. S., Bettie B. S., Gansbacher, Bernd, Blasberg, Ronald, Haugland, H. K., Saraste, J., Rooseni, K., Laerum, O. D., Vincent, A. J. P. E., Avezaat, C. J. J., Bout, A., Noteboom, J. L., Vecht, C. h., Valerio, D., Hoogerbrugge, P. M., Weber, F., Reszka, R., Zhu, J., Walther, W., List, J., Schulz, W., Wolbers, J. G., Sterenborg, I. I. J. C. M., Kamphorst, W., van Gemert, M. J. C., van Alplien, H. A. M., Salander P., Bergenheim T., Henriksson R., Grant, R., Brazil, L., Thomas, R., Guerrero, D., Laing, R., Ashley, S., Brada, M., Schmidt B., Bauer B., Grau G., Bohnstedt, T., Frydrych A., Franz K., Lorenz R., Brandes, A., Amanzo, P. D'., Zampieri, P., Rigon, A., Scelzi, E., Rotilio, A., Berti, F., Paccagnella, A., Fiorentino, M. V., Müller B., Krauseneck P., van Deventer, P. L., Dellemijn, P. L. I., van den Bent, M. J., Vecht, Ch. J., Kansen, P. J., Tredici, G., Petruccioli, N. G., Cavaletti, G., Cavalletti, E., Kiburg, B., Müller, L. J., Moorer-van Delft, C. M., Heimans, J. J., Boer, H. H., Pace A., Bove L., Pietrangeli A., Innocenti P., Aloe A., Nardi M., Jandolo B., Kellie S. J., De Graaf S. S. N., Bloemhof H., Roebuck D., Dalla Pozza L., Uges D. D. R., Johnston I., Besser M., Chaseling R. A., Koeppen, S., Gründemann, S., Lossos, A., Siegal, T., Nitschke M., Vieregge P., Reusche E., Rob P., Kömpf D., Postma, T. J., Vermorken, J. B., Heimans, J. J., Rampling R. P., Dunlop D. J., Steward M. S., Campbell S. M., Roy S., Hilkens, P. H. E., Verweij, J., van Putten, W. L. J., Vecht, Ch. J., van den Bent, M. J., Hilkens, P. H. E., Moll, J. W. B., van der Burg, M. E. L., Planting, A. S. T., van Putten, W. L. J., Vecht, Ch. J., van den Bent, M. J., Wondrusch E., Zifko U., Drlicek M., Liszka U., Grisold W., Zifko U., Fazeny B., Dittrich Ch., Wondrusch E., Grisold W., Verschuuren, Jan J., Meneses, Patricio I., Rosenfeld, Myrna R., Kaplitt, Michael G., Posner, Jerome B., Dalmau, Josep, Sillevis Smitt P. A. E., Manley G., Posner J. B., Cavaletti, G., Bogliun, G., Margorati, L., Bianchi, G., Drlicek, M., Liska, U., Casati, B., Kolig, C., Grisold, H., Graus, F., Reñe, R., Uchuya, M., Valldeoriola, F., Delattre, J. Y., Benedetti de Cosentiro C., Ortale D., Martinez R., Lambre J., Cagnolati S., Vinai C., Salmaggi A., Nemni R., Silvani A., Forno M. G., Luksch R., Confalonieri P., Boiardi A., Nitschke M., Scholz J., Vieregge P., Kömpf D., Hochberg F. H., Pfeiffer, G., Netzer, J., Hansen, Ch., Eggers, Ch., Hagel Ch., Kunze, K., Verschuuren, Jan J., Rosenblum, Marc K., Lieberman, Frank S., Posner, Jerome B., and Dalmau, Josep

Published
1994
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30. Inferior alveolar nerve trajectory, mental foramen location and incidence of mental nerve anterior loop

Author

Pablo Galindo-Moreno, Andrés Catena, García-Delgado R, Miguel Padial-Molina, Gustavo Avila-Ortiz, and Miguel Velasco-Torres

Subjects
0301 basic medicine, Adult, Male, Chin, Adolescent, Mandibular Nerve, Mandibular canal, Inferior alveolar nerve, Mandibular first molar, Mental foramen, Mandibular second molar, 03 medical and health sciences, Young Adult, 0302 clinical medicine, stomatognathic system, Premolar, Medicine, Humans, General Dentistry, UNESCO:CIENCIAS MÉDICAS, Aged, Retrospective Studies, Aged, 80 and over, business.industry, Research, Mandible, 030206 dentistry, Anatomy, Cone-Beam Computed Tomography, Middle Aged, Mental nerve, medicine.anatomical_structure, Cross-Sectional Studies, Otorhinolaryngology, Surgery, Female, 030101 anatomy & morphology, Oral Surgery, business
Abstract

Background: Injury of the inferior alveolar nerve (IAN) is a serious intraoperative complication that may occur during routine surgical procedures, such as dental implant placement or extraction of impacted teeth. Thus, the purpose of this study was to analyze the trajectory of the mandibular canal (MC), the location of the mental foramen (MF) and the presence and extension of an anterior loop of the mental nerve (AL). Study Design: In this cross-sectional study, a total of 348 CBCTs were analyzed. Distances from MC to the surface of the basal, medial and lateral cortical of the mandible were measured at the level of the second molar, first molar and second premolar. Location of the MF relative to the apices of the premolars, as well as incidence and anterior extent of the AL were also determined. Results: Significant and clinically relevant correlations were found between the position of the MC in women, which was located more caudal (r=-0.219, p=0.007; r=-0.276, p

Published
2017

31. Invariant metrics on central extensions of quadratic Lie algebras.

Author

García-Delgado, R., Salgado, G., and Sánchez-Valenzuela, O. A.

Subjects
*LIE algebras, *JORDAN algebras, *BILINEAR forms
Abstract

A quadratic Lie algebra is a Lie algebra endowed with a symmetric, invariant and nondegenerate bilinear form; such a bilinear form is called an invariant metric. The aim of this work is to describe the general structure of those central extensions of quadratic Lie algebras which in turn have invariant metrics. The structure is such that the central extensions can be described algebraically in terms of the original quadratic Lie algebra, and geometrically in terms of the direct sum decompositions that the invariant metrics involved give rise to. [ABSTRACT FROM AUTHOR]

Published
2020
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32. Generalized derivations and some structure theorems for Lie algebras.

Author

Dorado-Aguilar, E., García-Delgado, R., Martínez-Sigala, E., Rodríguez-Vallarte, M. C., and Salgado, G.

Subjects
*LIE algebras
Abstract

In this work, we show that the existence of invertible generalized derivations impose strong restrictions on the structure of a complex finite-dimensional Lie algebra. In particular, we recover the fact that a real Lie algebra admitting an abelian complex structure is necessarily solvable. On the other hand, we state a structure theorem for a Lie algebra 𝔤 admitting a periodic generalized derivation D ∈ Der (− 1 , 1 , 1) (𝔤). [ABSTRACT FROM AUTHOR]

Published
2020
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33. P12.03: Fetal congenital imperforate hymen

Author

Garcia Rodriguez, R., primary, García Delgado, R., additional, Rodríguez Guedes, A., additional, Pérez González, J., additional, Medina Castellano, M., additional, Segura González, J., additional, De Luis Alvarado, M., additional, and Ortega Cárdenes, I., additional

Published
2017
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35. EP09.04: Solitary median maxillary central incisor syndrome (SMMCI) in association with agenesis of the corpus callosum

Author

Medina Castellano, M., primary, García Delgado, R., additional, Garcia Rodriguez, R., additional, García Cruz, L., additional, Santana Rodríguez, A., additional, Novoa, Y., additional, Pérez González, J., additional, Segura González, J., additional, De Luis Alvarado, M., additional, and Ortega Cárdenes, I., additional

Published
2017
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36. P07.07: Ultrasound imaging of transobturator suburethral tape and its association with surgical outcome

Author

Ortega Cárdenes, I., primary, Medina Castellano, M., additional, Martínez, A.M., additional, García Hernandez, J., additional, Laseca Modrego, M., additional, Santana Suárez, A., additional, Pérez Morales, E., additional, Madsen Choppi, M., additional, Fernández Mederos, A., additional, García Delgado, R., additional, and Garcia Rodriguez, R., additional

Published
2017
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