Remarks on formal deformations and Batalin-Vilkovisky algebras
Vadim Schechtman
TL;DR
This paper discusses the structure of Batalin-Vilkovisky algebras on polyvector fields of Calabi-Yau manifolds and explores generalizations of this structure, highlighting its mathematical significance.
Contribution
It provides an exposition of Drinfeld's work on BV algebra structures and extends these ideas to broader contexts.
Findings
Polyvector fields on Calabi-Yau manifolds form BV algebras.
The paper generalizes the BV algebra structure beyond the initial setting.
It clarifies the relationship between sheaf structures and algebraic operations.
Abstract
This note consists of two parts. Part I is an exposition of (a part of) the V.Drinfeld's letter, [D]. The sheaf of algebras of polyvector fields on a Calabi-Yau manifold, equipped with the Schouten bracket, admits a structure of a Batalin-Vilkovisky algebra. This fact was probably first noticed by Z.Ran, [R]. Part II is devoted to some generalizations of this remark.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology