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Your search keyword '"Kontsevich formality"' showing total 4 results
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4 results on '"Kontsevich formality"'

1. BV formality.

Author

Campos, Ricardo

Subjects
*MATHEMATICAL analysis, *MATHEMATICS theorems, *MANIFOLDS (Mathematics), *HOMOTOPY equivalences, *ALGEBRAIC functions
Abstract

We prove a stronger version of the Kontsevich Formality Theorem for orientable manifolds, relating the Batalin–Vilkovisky (BV) algebra of multivector fields and the homotopy BV algebra of multidifferential operators of the manifold. [ABSTRACT FROM AUTHOR]

Published
2017
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2. L∞-formality check for the Hochschild complex of certain universal enveloping algebras.

Author

Bordemann, Martin, Elchinger, Olivier, Gutt, Simone, and Makhlouf, Abdenacer

Subjects
*UNIVERSAL algebra, *LIE algebras
Abstract

We study the L ∞ -formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more detail so (3)), and free Lie algebras. We show that for these examples formality in Kontsevich's sense does NOT hold, but we compute the L ∞ structure on the cohomology given by homotopy transfer in certain cases. [ABSTRACT FROM AUTHOR]

Published
2023
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3. Formalité linéaire analytique

Author

Mabrouka Hfaiedh, Didier Arnal, Mouna Chaabouni, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Laboratoire d'Analyse Harmonique de Sfax, Faculté des Sciences de Sfax, Université de Sfax - University of Sfax-Université de Sfax - University of Sfax, and Université de Sfax - University of Sfax

Subjects
Linear formality, Pure mathematics, Kontsevich formality, 010102 general mathematics, Subalgebra, General Medicine, Formality, 16. Peace & justice, analyticity, 01 natural sciences, Mathematics::Quantum Algebra, 53D50, 53D55, 05C30, 0103 physical sciences, 010307 mathematical physics, 0101 mathematics, Algebra over a field, [MATH]Mathematics [math], Mathematics
Abstract

International audience; In this paper, we study the restriction of the Kontsevich formality to the subalgebra of the linear polyvectors in the algebra of polyvector fields on Rd.We prove that this formality is an analytic map.; Dans ce papier nous étudions la restriction de la formalité de Kontsevich à la sous-algèbre des tenseurs linéaires, dans l’algèbre de Lie des tenseurs surRd. On établit que c’est une formalité analytique.

Published
2019
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4. Gravity formality

Author

Campos, Ricardo, Ward, Benjamin C., Campos, Ricardo, and Ward, Benjamin C.

Abstract

We show that Willwacher's cyclic formality theorem can be extended to preserve natural Gravity operations on cyclic multivector fields and cyclic multidifferential operators. We express this in terms of a homotopy Gravity quasiisomorphism with explicit local formulas. For this, we develop operadic tools related to mixed complexes and cyclic homology and prove that the operad M(O )of natural operations on cyclic operators is formal and hence quasi-isomorphic to the Gravity operad.

Published
2018
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