Gerstenhaber algebras and BV-algebras in Poisson geometry

Research output: Contribution to journalArticle

76 Citations (Scopus)

Abstract

The purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well-known algebraic structures such as Gerstenhaber algebras and BV-algebras. Some applications are discussed. In particular, we find an explicit connection between the Koszul-Brylinski operator and the modular class of a Poisson manifold. As a consequence, we prove that Poisson homology is isomorphic to Poisson cohomology for unimodular Poisson structures.

Original languageEnglish (US)
Pages (from-to)545-560
Number of pages16
JournalCommunications In Mathematical Physics
Volume200
Issue number3
DOIs
StatePublished - Jan 1 1999

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Gerstenhaber Algebra
Poisson Geometry
homology
Siméon Denis Poisson
algebra
Poisson Manifolds
Algebra
Poisson Structure
Geometric Structure
geometry
Algebraic Structure
Vector Bundle
bundles
Cohomology
Homology
Correspondence
Isomorphic
operators
Operator

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Gerstenhaber algebras and BV-algebras in Poisson geometry. / Xu, Ping.

In: Communications In Mathematical Physics, Vol. 200, No. 3, 01.01.1999, p. 545-560.

Research output: Contribution to journalArticle

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