Displaying similar documents to “Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects”

Coalgebraic Approach to the Loday Infinity Category, Stem Differential for 2 n -ary Graded and Homotopy Algebras

Mourad Ammar, Norbert Poncin (2010)

Annales de l’institut Fourier

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We define a graded twisted-coassociative coproduct on the tensor algebra the desuspension space of a graded vector space V . The coderivations (resp. quadratic “degree 1” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1-to-1 with sequences of multilinear maps on V (resp. graded Loday structures on V , sequences that we call Loday infinity structures on V ). We prove a minimal model theorem for Loday infinity algebras and observe that the Lod ∞ category contains the L ∞ ...

Deformations of Batalin-Vilkovisky algebras

Olga Kravchenko (2000)

Banach Center Publications

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We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of a Batalin-Vilkovisky algebra. While such an operator of order 2 defines a Gerstenhaber (Lie) algebra structure on A, an operator of an order higher than 2 (Koszul-Akman definition) leads to the structure of a strongly homotopy Lie algebra ( L ∞ -algebra) on A. This allows us to give a definition of a Batalin-Vilkovisky algebra up to homotopy. We also make a conjecture...

Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications

Jian Qiu, Maxim Zabzine (2011)

Archivum Mathematicum

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These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration...

On the cohomology of vector fields on parallelizable manifolds

Yuly Billig, Karl-Hermann Neeb (2008)

Annales de l’institut Fourier

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In the present paper we determine for each parallelizable smooth compact manifold M the second cohomology spaces of the Lie algebra 𝒱 M of smooth vector fields on M with values in the module Ω ¯ M p = Ω M p / d Ω M p - 1 . The case of p = 1 is of particular interest since the gauge algebra of functions on M with values in a finite-dimensional simple Lie algebra has the universal central extension with center Ω ¯ M 1 , generalizing affine Kac-Moody algebras. The second cohomology H 2 ( 𝒱 M , Ω ¯ M 1 ) classifies twists of the semidirect product...