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The question we address in this paper is: which monomial ideals have minimal cellular resolutions, that is, minimal resolutions obtained from homogenizing the chain maps of CW-complexes? Velasco gave families of examples of monomial ideals that do not have minimal cellular resolutions, but those examples have large minimal generating sets. In this paper, we show that if a monomial ideal has at most four generators, then the ideal and its (monomial) Artinian reductions have minimal cellular resolutions. When the ideal is generated by two monomials, we can give a precise description of the CW-complex supporting minimal free resolution of the ideal and its Artinian reduction. Also, in this case, we compute the multigraded Betti numbers, Cohen-Macaulay type and determine when the corresponding algebra is a level algebra. [ABSTRACT FROM AUTHOR]

In the present paper we investigate reflexive modules over the endomorphism algebras of reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem generalizes both of the results of S. Goto, N. Matsuoka, and T. T. Phuong ([20, Theorem 5.1]) and T. Kobayashi ([30, Theorem 1.3]) concerning the endomorphism algebra of its maximal ideal. We also explore the question of when the category of reflexive modules is of finite type, i.e., the base ring has only finitely many isomorphism classes of indecomposable reflexive modules. We show that, if the category is of finite type, the ring is analytically unramified and has only finitely many Ulrich ideals. As a consequence, Arf local rings contain only finitely many Ulrich ideals once the normalization is a local ring. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new invariant for a non-degenerate evolution algebra, which consists of an ordered sequence of evolution algebras of lower dimension, belonging all of them to a specific family. We use this invariant to propose a method to classify non-degenerate evolution algebras, and we apply it up to dimension 3. We also use it to describe the derivations of some families of evolution algebras and the degenerations of the variety of evolution algebras with square not greater than 1. [ABSTRACT FROM AUTHOR]

Given a finite dimensional algebra A over a field k , and a finite acyclic quiver Q , let Λ = A ⊗ k k Q / I , where kQ is the path algebra of Q over k and I is a monomial ideal. This paper is devoted to studying the separated monic representations over the bounded quiver (Q , I) over a subcategory X of A -mod, denoted by smon (Q , I , X). We show that (X , Y) is a (complete) hereditary cotorsion pair in A -mod if and only if (smon (Q , I , X) , rep (Q , I , Y)) is a (complete) hereditary cotorsion pair in Λ-mod. We also show that A is left weakly Gorenstein if and only if so is Λ. Provided that k Q / I is non-semisimple, the category ▪ of semi-Gorenstein-projective Λ-modules coincides with the category of separated monic representations ▪ if and only if A is left weakly Gorenstein. [ABSTRACT FROM AUTHOR]

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an algebraic and geometric investigation of these polytopes by studying their toric algebras, called cycle algebras, and their defining ideals. Several matroid operations are considered which determine faces of cycle polytopes that belong again to this class of polyhedral objects. As a key technique used in this paper, we study certain minors of given matroids which yield algebra retracts on the level of cycle algebras. In particular, that allows us to use a powerful algebraic machinery. As an application, we study highest possible degrees in minimal homogeneous systems of generators of defining ideals of cycle algebras as well as interesting cases of cut polytopes and Eulerian subgraph polytopes. [ABSTRACT FROM AUTHOR]

In a previous paper, we presented an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley–Lieb algebra having a basis indexed by the fully commutative elements of the Coxeter group of type affine C . We also provided an explicit description of a basis for the diagram algebra. In this paper, we show that the diagrammatic representation is faithful and establish a correspondence between the basis diagrams and the so-called monomial basis of the Temperley–Lieb algebra of type affine C . [ABSTRACT FROM AUTHOR]

The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity rely on a pairing – the embedding tensor – between a Leibniz algebra and a Lie algebra. Two such algebras, together with their embedding tensor, form a triple called a Lie-Leibniz triple , of which Lie algebra crossed modules are particular cases. This paper is devoted to showing that any Lie-Leibniz triple induces a differential graded Lie algebra – its associated tensor hierarchy – whose restriction to the category of Lie algebra crossed modules is the canonical assignment associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of 'lie-ization' of the former. We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations. We stress that such a construction suggests the existence of further well-defined Leibniz gauge theories. [ABSTRACT FROM AUTHOR]

We make several corrections and improvements to the published paper "Combinatorial categorical equivalences of Dold–Kan type", mostly relating to the standing assumptions of the paper. In particular we have had to add one new assumption, but have been able to remove another. [ABSTRACT FROM AUTHOR]

Let X be a quasi-compact, separated scheme over a field k and we can consider the categorical resolution of singularities of X . In this paper let k ′ / k be a field extension and we study the scalar extension of a categorical resolution of singularities of X and we show how it gives a categorical resolution of the base change scheme X k ′ . Our construction involves the scalar extension of derived categories of DG-modules over a DG algebra. As an application we use the technique of scalar extension developed in this paper to prove the non-existence of full exceptional collections of categorical resolutions for a projective curve of genus ≥1 over a non-algebraically closed field. [ABSTRACT FROM AUTHOR]

Let KQ be a path algebra, where Q is a finite quiver and K is a field. We study K Q / C where C is the two-sided ideal in KQ generated by all differences of parallel paths in Q. We show that K Q / C is always finite dimensional and its global dimension is finite. Furthermore, we prove that K Q / C is Morita equivalent to an incidence algebra. The paper starts with a more general setting, where KQ is replaced by K Q / I with I a two-sided ideal in KQ. [ABSTRACT FROM AUTHOR]

The rigidity degree of a generator-cogenerator determines the dominant dimension of its endomorphism algebra, and is closely related to a recently introduced homological dimension — rigidity dimension. In this paper, we give explicit formulae for the rigidity degrees of all indecomposable modules over representation-finite self-injective algebras by developing combinatorial methods from the Euclidean algorithm. As an application, the rigidity dimensions of some algebras of types A and E are given. [ABSTRACT FROM AUTHOR]

The statements of Theorem 6.11 and Theorem 7.8 in the published paper are not correct: each have a missing hypothesis which is needed for their proof. We restate both theorems (with the required extra hypothesis), and give corrected proofs of each. [ABSTRACT FROM AUTHOR]

In a previous paper the authors constructed a class of quasi-Hopf algebras D ω (G , A) associated to a finite group G , generalizing the twisted quantum double construction. We gave necessary and sufficient conditions, cohomological in nature, that the corresponding module category Rep (D ω (G , A)) is a modular tensor category. In the present paper we verify the cohomological conditions for the class of groups G which contain a unique involution , and in this way we obtain an explicit construction of a new class of modular quasi-Hopf algebras. We develop the basic theory for general finite groups G , and also a parallel theory concerned with the question of when Rep (D ω (G , A)) is super-modular rather than modular. We give some explicit examples involving binary polyhedral groups and some sporadic simple groups. [ABSTRACT FROM AUTHOR]

In this paper, we characterize suitable partial (co)actions of Taft and Nichols Hopf algebras on algebras, and moreover we get that such partial (co)actions are symmetric. For certain algebras, these partial (co)actions obtained are, indeed, all of them. This work generalizes the results obtained by the authors in [16]. [ABSTRACT FROM AUTHOR]

The main goals for this paper are i) to study of the algebraic structure of N -graded vertex algebras V B associated with vertex A -algebroids B when B are cyclic non-Lie left Leibniz algebras, and ii) to explore relations between the vertex algebras V B and the rank one Heisenberg vertex operator algebra. To achieve these goals, we first classify vertex A -algebroids B associated with given cyclic non-Lie left Leibniz algebras B. Next, we use the constructed vertex A -algebroids B to create a family of indecomposable non-simple vertex algebras V B. Finally, we use the algebraic structure of the unital commutative associative algebras A that we found to study relations between certain types of the vertex algebras V B and the vertex operator algebra associated to the rank one Heisenberg algebra. [ABSTRACT FROM AUTHOR]

It is well-known that the construction of Zariski spectra of (commutative) rings yields a dual adjunction between the category of rings and the category of locally ringed spaces. There are many constructions of spectra of algebras in various contexts giving such adjunctions. Michel Coste unified them in the language of categorical logic by showing that, for an appropriate triple (T 0 , T , Λ) (which we call a spatial Coste context), each T 0 -model can be associated with a T -modelled space and that this yields a dual adjunction between the category of T 0 -models and the category of T -modelled spaces and "admissible" morphisms. However, most of his proofs remain unpublished. In this paper, we introduce an alternative construction of spectra of T 0 -models, which is reminiscent of Zariski spectra, and give a new proof of Coste adjunction. Moreover, we also extend spectra of T 0 -models to relative spectra of T 0 -modelled spaces and prove the existence of limits and colimits in the involved categories of modelled spaces. We can deduce, for instance, that the category of ringed spaces whose stalks are fields is complete and cocomplete. [ABSTRACT FROM AUTHOR]

In this paper we study the low dimensional cohomology groups of Hom-Lie algebras and their relation with derivations, abelian extensions and crossed modules. On one hand, we introduce the notion of α -abelian extensions and we obtain a five term exact sequence in cohomology. On the other hand, we study crossed modules of Hom-Lie algebras showing their equivalence with cat1-Hom-Lie algebras, and we introduce α -crossed modules to have a better understanding of the third cohomology group. [ABSTRACT FROM AUTHOR]

Hypergraph categories have been rediscovered at least five times, under various names, including well-supported compact closed categories, dgs-monoidal categories, and dungeon categories. Perhaps the reason they keep being reinvented is two-fold: there are many applications—including to automata, databases, circuits, linear relations, graph rewriting, and belief propagation—and yet the standard definition is so involved and ornate as to be difficult to find in the literature. Indeed, a hypergraph category is, roughly speaking, a "symmetric monoidal category in which each object is equipped with the structure of a special commutative Frobenius monoid, satisfying certain coherence conditions". Fortunately, this description can be simplified a great deal: a hypergraph category is simply a "cospan-algebra," roughly a lax monoidal functor from cospans to sets. The goal of this paper is to remove the scare-quotes and make the previous statement precise. We prove two main theorems. First is a coherence theorem for hypergraph categories, which says that every hypergraph category is equivalent to an objectwise-free hypergraph category. Second, we prove that the category of objectwise-free hypergraph categories is equivalent to the category of cospan-algebras. [ABSTRACT FROM AUTHOR]

Abstract In this paper we construct a ring A which has annihilator condition (a.c.) and we show that neither A [ x ] nor A [ [ x ] ] has this property. This answers in negative a question asked by Hong, Kim, Lee and Nielsen. We also show that there is an algebra A which does not have annihilator condition while both A [ x ] and A [ [ x ] ] have this property. [ABSTRACT FROM AUTHOR]

Abstract A convex code is a binary code generated by the pattern of intersections of a collection of open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as they arise from the activity of neurons that have convex receptive fields. In this paper, we develop algebraic methods to determine if a code is convex. Specifically, we use the neural ideal of a code, which is a generalization of the Stanley–Reisner ideal. Using the neural ideal together with its standard generating set, the canonical form , we provide algebraic signatures of certain families of codes that are non-convex. We connect these signatures to the precise conditions on the arrangement of sets that prevent the codes from being convex. Finally, we also provide algebraic signatures for some families of codes that are convex, including the class of intersection-complete codes. These results allow us to detect convexity and non-convexity in a variety of situations, and point to some interesting open questions. [ABSTRACT FROM AUTHOR]

The q -Onsager algebra O q is defined by two generators and two relations, called the q -Dolan/Grady relations. We investigate the alternating central extension O q of O q. The algebra O q was introduced by Baseilhac and Koizumi, who called it the current algebra of O q. Recently Baseilhac and Shigechi gave a presentation of O q by generators and relations. The presentation is attractive, but the multitude of generators and relations makes the presentation unwieldy. In this paper we obtain a presentation of O q that involves a subset of the original set of generators and a very manageable set of relations. We call this presentation the compact presentation of O q. This presentation resembles the compact presentation of the alternating central extension for the positive part of U q ( sl ˆ 2). [ABSTRACT FROM AUTHOR]

In this paper, we define a quotient of the cyclotomic Hecke algebra of type G (r , 1 , n) as a generalisation of the Temperley-Lieb algebras of type A and B. We establish a graded cellular structure for the generalised Temperley-Lieb algebra and, using the technology of KLR algebras, determine the corresponding decomposition matrix. [ABSTRACT FROM AUTHOR]

In this paper, a continuation of [24] , we investigate the S 3 -orbifold subalgebra of (V c) ⊗ 3 , that is, we consider the S 3 -fixed point vertex subalgebra of the tensor product of three copies of the universal Virasoro vertex operator algebras V c. Our main result is construction of a minimal, strong set of generators of this subalgebra for any generic values of c. More precisely, we show that this vertex algebra is of type (2 , 4 , 6 2 , 8 2 , 9 , 10 2 , 11 , 12 3). We also investigate two prominent examples of simple S 3 -orbifold algebras corresponding to central charges c = 1 2 (Ising model) and c = − 22 5 (i.e. (2 , 5) -minimal model). We prove that the former is a new unitary W -algebra of type (2 , 4 , 6 , 8) and the latter is isomorphic to the affine simple W -algebra of type G 2 at non-admissible level − 19 6. We also provide another version of this isomorphism using the affine W -algebra of type G 2 coming from a subregular nilpotent element. [ABSTRACT FROM AUTHOR]

States of unital Abelian lattice-groups (normalised positive group homomorphisms to R) provide an abstraction of expected-value operators. A well-known theorem due to Mundici asserts that the category of unital lattice-groups (with unit-preserving lattice-group homomorphisms as morphisms) is equivalent to the algebraic category of MV-algebras, and their homomorphisms. Through this equivalence, states of lattice-groups correspond to certain [ 0 , 1 ] -valued functionals on MV-algebras, which are also known as states. In this paper we allow states to take values in any unital lattice-group (or in any MV-algebra) rather than just in R (or just in [ 0 , 1 ] , respectively). We introduce a two-sorted algebraic theory whose models are precisely states of MV-algebras. We extend Mundici's equivalence to one between the category of MV-algebras with states as morphisms, and the category of unital Abelian lattice-groups with, again, states as morphisms. Thus, the models of our two-sorted theory may also be regarded as states between unital Abelian lattice-groups. As our first main result, we derive the existence of the universal state of any MV-algebra from the existence of free algebras in multi-sorted algebraic categories. The significance of the universal state of a given algebra is that it provides the most general expected-value operator on that algebra—a construct that is not available if one insists that states be real-valued. In the remaining part of the paper, we seek concrete representations of such universal states. We begin by clarifying the relationship of universal states with the theory of affine representations: the universal state A → B of the MV-algebra A coincides with a certain modification of Choquet's affine representation (of the lattice-group corresponding to A) if, and only if, B is semisimple. Locally finite MV-algebras are semisimple, and Boolean algebras are instances of locally finite MV-algebras. Our second main result is then that the universal state of any locally finite MV-algebra has semisimple codomain, and can thus be described through our adaptation of Choquet's affine representation. [ABSTRACT FROM AUTHOR]

Abstract: Convolutional codes have appeared in the literature endowed with sufficient additional algebraic structure to be considered as (left) ideals of a (code-ambient) automorphism-twisted polynomial ring with coefficients in a (word-ambient) semisimple finite group ring. In this paper we extend the present scope of the theory by considering a code-ambient twisted polynomial ring having, in addition to an automorphism , the action of a -derivation . In addition, we develop the basic theory without any specific restrictions for the semisimple finite word-ambient ring. This second element therefore extends even the original notions of both cyclic and group convolutional codes considered thus far in the literature. Among other results, in this paper we develop a matrix-based approach to the study of our extended notion of group convolutional codes (and therefore of cyclic convolutional codes as well), inspired by the use of circulant matrices by Gluesing-Luerssen and Schmale, and then use it to extend to this level the results on the existence of dual codes that were originally established by those authors for cyclic codes (in the narrower sense without a -derivation). Various examples illustrate the potential value of extending the search for good convolutional codes in this direction. [Copyright &y& Elsevier]

Abstract It is known that every 3-dimensional noetherian Calabi–Yau algebra generated in degree 1 is isomorphic to a Jacobian algebra of a superpotential. Recently, S.P. Smith and the first author classified all superpotentials whose Jacobian algebras are 3-dimensional noetherian quadratic Calabi–Yau algebras. The main result of this paper is to classify all superpotentials whose Jacobian algebras are 3-dimensional noetherian cubic Calabi–Yau algebras. As an application, we show that if S is a 3-dimensional noetherian cubic Calabi–Yau algebra and σ is a graded algebra automorphism of S , then the homological determinant of σ can be calculated by the formula hdet σ = (det σ) 2 with one exception. [ABSTRACT FROM AUTHOR]

Abstract In this paper we show how the colored Khovanov–Rozansky sl N -matrix factorizations, due to Wu [45] and Y.Y. [46,47] , can be used to categorify the type A quantum skew Howe duality defined by Cautis, Kamnitzer and Morrison in [14]. In particular, we define sl N -web categories and 2-representations of Khovanov and Lauda's categorical quantum sl m on them. We also show that this implies that each such web category is equivalent to the category of finite-dimensional graded projective modules over a certain type A cyclotomic KLR-algebra. [ABSTRACT FROM AUTHOR]

Abstract Let R be an affine domain of dimension n ≥ 3 over a field of characteristic 0 and D = R [ X , Y ] / (X Y). Let I ⊂ D be a local complete intersection ideal of height n such that μ (I / I 2) = n. This paper examines under what condition I is surjective image of a projective D -module of rank n. [ABSTRACT FROM AUTHOR]

Abstract Let I ⊆ k [ x 1 , ... , x n ] be a squarefree monomial ideal in a polynomial ring. In this paper we study multiplications on the minimal free resolution F of k [ x 1 , ... , x n ] / I. In particular, we characterize the possible vectors of total Betti numbers for such ideals which admit a differential graded algebra (DGA) structure on F. We also show that under these assumptions the maximal shifts of the graded Betti numbers are subadditive. On the other hand, we present an example of a strongly generic monomial ideal which does not admit a DGA structure on its minimal free resolution. In particular, this demonstrates that the Hull resolution and the Lyubeznik resolution do not admit DGA structures in general. Finally, we show that it is enough to modify the last map of F to ensure that it admits the structure of a DG algebra. [ABSTRACT FROM AUTHOR]

Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing “mesoprimary decompositions” determined by their underlying monoid congruences. Monoid congruences (and therefore, binomial ideals) can present many subtle behaviors that must be carefully accounted for in order to produce general results, and this makes the theory complicated. In this paper, we examine their results in the presence of a positive A -grading, where certain pathologies are avoided and the theory becomes more accessible. Our approach is algebraic: while key notions for mesoprimary decomposition are developed first from a combinatorial point of view, here we state definitions and results in algebraic terms, which are moreover significantly simplified due to our (slightly) restricted setting. In the case of toral components (which are well-behaved with respect to the A -grading), we are able to obtain further simplifications under additional assumptions. We also provide counterexamples to two open questions, identifying (i) a binomial ideal whose hull is not binomial, answering a question of Eisenbud and Sturmfels, and (ii) a binomial ideal I for which I toral is not binomial, answering a question of Dickenstein, Miller and the first author. [ABSTRACT FROM AUTHOR]

The filtered derived category of an abelian category has played a useful role in subjects including geometric representation theory, mixed Hodge modules, and the theory of motives. We develop a natural generalization using current methods of homotopical algebra, in the formalisms of stable ∞-categories, stable model categories, and pretriangulated, idempotent-complete dg categories. We characterize the filtered stable ∞-category Fil ( C ) of a stable ∞-category C as the left exact localization of sequences in C along the ∞-categorical version of completion (and prove analogous model and dg category statements). We also spell out how these constructions interact with spectral sequences and monoidal structures. As examples of this machinery, we construct a stable model category of filtered D -modules and develop the rudiments of a theory of filtered operads and filtered algebras over operads. This paper is also available at arXiv:1602.01515v3 . [ABSTRACT FROM AUTHOR]

Abstract: Ariki, Mathas and Rui [S. Ariki, A. Mathas, H. Rui, Cyclotomic Nazarov–Wenzl algebras, Nagoya Math. J. 182 (2006) 47–134 (special volume in honor of Professor G. Lusztig)] introduced a class of finite dimensional algebras , called the cyclotomic Nazarov–Wenzl algebras which are associative algebras over a commutative ring generated by satisfying the defining relations given in this paper. In particular, for any positive integers . Note that are quotients of affine Wenzl algebras in [M. Nazarov, Young’s orthogonal form for Brauer’s centralizer algebra, J. Algebra 182 (1996) 664–693]. It has been proved in the first cited reference above that is cellular in the sense of [J.J. Graham, G.I. Lehrer, Cellular algebras, Invent. Math. 123 (1996) 1–34]. Using the representation theory of cellular algebras, Ariki, Mathas and Rui have classified the irreducible -modules under the assumption in their above-cited work. In this paper, we are going to classify the irreducible -modules under the assumption . We will compute the Gram determinant associated to each cell module for no matter whether is zero or not. At the end of this paper, we use our formulae for Gram determinants to determine the semisimplicity of for arbitrary parameters over an arbitrary field with . [Copyright &y& Elsevier]

Abstract: The locus in the moduli space of curves where the Petri map fails to be injective is called the Petri locus. In this paper we provide a new proof on the existence of Divisorial components in the Petri locus for the case of pencils. For this proof we produce some special reducible curves (chains of elliptic components) in the Petri locus and we show that such curves have only a finite number of pencils for which the Petri map is not injective. [Copyright &y& Elsevier]

Abstract: It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675–686] that, for any odd prime , every finite group of even order has a non-trivial rational-valued irreducible -Brauer character. For this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if are primes, then any finite group of order divisible by has a non-trivial irreducible -Brauer character with values in the cyclotomic field . [Copyright &y& Elsevier]

Abstract: Recent work of Janelidze and Sobral on descent theory of finite topological spaces motivated our interest in ultrafilter descriptions of various classes of continuous maps. In earlier papers we presented such characterizations for triquotient maps and local homeomorphisms, here we do it for regular epimorphisms. To do so, we give an alternative description of the “obvious” reflection of pseudotopological spaces into topological spaces. Topological spaces, when presented as ultrafilter convergence structures, are examples of -algebras introduced by Clementino and Tholen in “Metric, Topology and Multicategory—a Common Approach”. In this paper, we work in this general setting and hence obtain at once characterizations of regular epimorphisms between topological spaces, approach spaces and (generalized) metric spaces, as well as the characterization for preordered sets which motivated our work. [Copyright &y& Elsevier]

In this paper we give a general theorem that describes necessary and sufficient conditions for a module to satisfy the so-called Kadison–Dubois property. This is used to generalize Jacobi''s version of the Kadison–Dubois representation to associative rings. We apply this representation to obtain a noncommutative algebraic and geometric version of Putinar''s Positivstellensatz. We finish the paper by answering questions given by Marshall and Jacobi. [Copyright &y& Elsevier]

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Such a polynomial is always a product of linear factors over K, although not every product of linear polynomials is a Wedderburn polynomial. In this paper, we establish various properties and characterizations of Wedderburn polynomials over K, and show that these polynomials form a complete modular lattice that is dual to the lattice of full algebraic subsets of K. Throughout the paper, we work in the general setting of an Ore skew polynomial ring K[t,S,D], where S is an endomorphism of K and D is an S-derivation on K. [Copyright &y& Elsevier]

For coalgebras over fields, there is a well-known construction which gives the cofree coalgebra over a vector space as a certain completion of the tensor coalgebra. In the case of a one-dimensional vector space this is the coalgebra of recursive sequences. In this paper, it is shown that similar ideas work in the multivariable case over rings (instead of fields). In particular, this paper contains a notion of recursiveness that exactly fits. For the case of a finite number of noncommuting variables over a field, it is the same as Schu¨tzenberger recognizability. There are applications to the question of the main theorem of coalgebras for coalgebras over rings. As should be the case, the cofree coalgebra over a finitely generated free module over a ring is the ‘zero dual’ of the free algebra over that module. A final application is a faithful representation theorem for coalgebras, that is representing a coalgebra as a subcoalgebra of a matrix-like coalgebra. [Copyright &y& Elsevier]

This paper contains results on asymmetries of anti-automorphisms of central simple algebras, following on from a recent paper of Cortella and Tignol, and also some properties of trace forms of anti-automorphisms. [Copyright &y& Elsevier]

This paper pursues the study of the pseudo-supports of a finitely generated module over a finite-dimensional commutative Noetherian ring, and is particularly concerned with the properties of the pseudo-supports of a geometric normal local domain. It is shown that these pseudo-supports have certain properties that can be summarized by the so-called occurrence diagram of the ring, which is a certain subset of N0×N0. Standard properties of local cohomology modules enable one to conclude that there are obvious restrictions on the type of subset of N0×N0 that can be an occurrence diagram in this way, and much of the paper is devoted to consideration of whether a subset of N0×N0 that meets those obvious restrictions is an occurrence diagram of some geometric normal local domain. These occurrence diagrams are also used to assist with the production of examples that show that a question raised by C. Huneke, about certain sets related to Grothendieck''s Finiteness Theorem for local cohomology, has a negative answer. [Copyright &y& Elsevier]

Slim cyclotomic q -Schur algebras are certain centralizer subalgebras of cyclotomic q -Schur algebras in the sense of Dipper, James and Mathas, including q -Schur algebras of type A and C as examples. In the present paper we provide a sufficient condition for a slim cyclotomic q -Schur algebra S m (n , r) to be quasi-hereditary. More precisely, it is shown that S m (n , r) is quasi-hereditary if the cyclotomic Hecke algebra has a semisimple bottom. Moreover, we prove that S m (1 , r) is quasi-hereditary if and only if the cyclotomic Hecke algebra has a semisimple bottom. In the case where m = n = r = 2 and q = ± 1 , we prove that this condition is also necessary. [ABSTRACT FROM AUTHOR]

In this paper, we determine the modular invariants for some pseudo-reflection subgroups of the finite general linear group GL n (q) acting on the tensor product of the symmetric algebra S • (V) and the exterior algebra ∧ • (V) of the natural GL n (q) -module V. We are particularly interested in the case when the pseudo-reflection groups are subgroups of the parabolic subgroup of GL n (q) which are generalization of Weyl groups of Cartan type Lie algebra. [ABSTRACT FROM AUTHOR]

This paper studies restricted modules of gap- p Virasoro algebra g p and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted g p -modules of level ℓ _ and the category of twisted modules of vertex algebra V N p (ℓ _ , 0) , where N p is a new Lie algebra, ℓ _ : = (ℓ 0 , 0 , ⋯ , 0) ∈ C [ p 2 ] + 1 , ℓ 0 ∈ C is the action of the Virasoro center. Then we focus on the construction and classification of simple restricted g p -modules of level ℓ _. More explicitly, we give a uniform construction of simple restricted g p -modules as induced modules. We present several equivalent characterizations of simple restricted g p -modules, as locally nilpotent (equivalently, locally finite) modules with respect to certain positive part of g p. Moreover, simple restricted g p -modules of level ℓ _ are classified. They are either highest weight modules or simple induced modules. At the end, we exhibit several concrete examples of simple restricted g p -modules of level ℓ _ (including Whittaker modules). [ABSTRACT FROM AUTHOR]

In this paper, we compute Gram determinants associated to all cell modules of quantized walled Brauer algebras B r , t (ρ , q) over an arbitrary field κ. Suppose e is the quantum characteristic of q 2. We classify the blocks of B r , t (ρ , q) when e > max ⁡ { r , t } and ρ 2 = q 2 n , n ∈ Z. As an application, we give a criterion for a cell module of B r , t (ρ , q) being equal to its simple head over κ. [ABSTRACT FROM AUTHOR]

Let U ( gl ˆ n) be the universal enveloping algebra of gl ˆ n. A certain Z -form U Z ( gl ˆ n) of U ( gl ˆ n) was introduced in [15] such that the affine Schur algebra S ▵ (n , r) Z is a homomorphic image of U Z ( gl ˆ n). Let k be a field and let U k ( gl ˆ n) = U Z ( gl ˆ n) ⊗ k. Let S ▵ (n , r) k = S ▵ (n , r) Z ⊗ k. By tensoring with k , we have a surjective algebra homomorphism ξ r , k : = ξ r ⊗ i d : U k ( gl ˆ n) ↠ S ▵ (n , r) k. For h ⩾ 1 and r ∈ N let s ▵ (n , r) h = ξ r , k (s ▵ (n) h) , where s ▵ (n) h is a certain subalgebra of U k ( gl ˆ n). The algebra s ▵ (n , r) h is the affine analogue of infinitesimal Schur algebras introduced in [7]. In this paper we will give a presentation of s ▵ (n , r) 1 by generators and defining relations. [ABSTRACT FROM AUTHOR]

In a previous paper (Pure Appl. Algebra 159 (2001) 231) a definition of point of a Gelfand quantale is given in terms of algebraically irreducible representations of the quantale on an atomic orthocomplemented sup-lattice. The definition yields the usual notion of point when applied to a locale viewed as a quantale and helps to establish that the spectrum Max A of a C*-algebra A is an invariant of A. The current paper is concerned with finding a notion of spatiality in which, as intuitively expected, Max A is spatial, and for which there is an intimate connection with points in the above sense. Moreover, the approach taken relates naturally to that of Giles and Kummer in their article on non-commutative spaces (Indiana Math. J. 21 (1971) 91). Explicitly, an involutive unital quantale X is said to be spatial provided that it admits an algebraically strong right embedding into a discrete von Neumann quantale Q. It is proved that X is spatial if, and only if, it has enough points, and that, in this case, it is necessarily a Gelfand quantale. In particular, a locale is spatial as an involutive unital quantale precisely when it yields the topology of a classical topological space. A notion of quantal space is defined, and it is shown that any involutive unital quantale admits a spatialisation determined by its points, generalising that known for locales. In particular, any quantal space admits an underlying topological space. Finally, Max A is shown to be spatial, and to determine a canonical quantal space, as desired. [Copyright &y& Elsevier]

A code algebra A C is a nonassociative commutative algebra defined via a binary linear code C. In a previous paper, we classified when code algebras are Z 2 -graded axial (decomposition) algebras generated by small idempotents. In this paper, for each algebra in our classification, we obtain the Miyamoto group associated to the grading. We also show that the code algebra structure can be recovered from the axial decomposition algebra structure. [ABSTRACT FROM AUTHOR]

In this paper we describe the defining equations of the multi-Rees algebra R [ { I n i t i } 1 ≤ i ≤ r ] over a Noetherian ring R when I is an ideal of linear type. This generalizes a result of Ribbe and recent work of Lin–Polini and Sosa. [ABSTRACT FROM AUTHOR]

Let K be the algebraic closure of a finite field F q of odd characteristic p . For a positive integer m prime to p , let F = K ( x , y ) be the transcendence degree 1 function field defined by y q + y = x m + x − m . Let t = x m ( q − 1 ) and H = K ( t ) . The extension F | H is a non-Galois extension. Let K be the Galois closure of F with respect to H . By Stichtenoth [20] , K has genus g ( K ) = ( q m − 1 ) ( q − 1 ) , p -rank (Hasse–Witt invariant) γ ( K ) = ( q − 1 ) 2 and a K -automorphism group of order at least 2 q 2 m ( q − 1 ) . In this paper we prove that this subgroup is the full K -automorphism group of K ; more precisely Aut K ( K ) = Δ ⋊ D where Δ is an elementary abelian p -group of order q 2 and D has an index 2 cyclic subgroup of order m ( q − 1 ) . In particular, m | Aut K ( K ) | > g ( K ) 3 / 2 , and if K is ordinary (i.e. g ( K ) = γ ( K ) ) then | Aut K ( K ) | > g 3 / 2 . On the other hand, if G is a solvable subgroup of the K -automorphism group of an ordinary, transcendence degree 1 function field L of genus g ( L ) ≥ 2 defined over K , then | Aut K ( K ) | ≤ 34 ( g ( L ) + 1 ) 3 / 2 < 68 2 g ( L ) 3 / 2 ; see [15] . This shows that K hits this bound up to the constant 68 2 . Since Aut K ( K ) has several subgroups, the fixed subfield F N of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in Aut K ( K ) is large enough. This possibility is worked out for subgroups of Δ. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence problem of rank one and two stable Ulrich bundles on imprimitive Fano 3-folds obtained by blowing-up one of P 3 , Q (smooth quadric in P 4 ), V 3 (smooth cubic in P 4 ) or V 4 (complete intersection of two quadrics in P 5 ) along a smooth irreducible curve. We prove that the only class which admits Ulrich line bundles is the one obtained by blowing up a genus 3, degree 6 curve in P 3 . Also, we prove that there exist stable rank two Ulrich bundles with c 1 = 3 H on a generic member of this deformation class. [ABSTRACT FROM AUTHOR]