Gerstenhaber algebras and BV-algebras in Poisson geometry

Ping Xu

doi:10.1007/s002200050540

Gerstenhaber algebras and BV-algebras in Poisson geometry

Ping Xu

Research output: Contribution to journal › Article › peer-review

80 Scopus citations

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 language	English (US)
Pages (from-to)	545-560
Number of pages	16
Journal	Communications In Mathematical Physics
Volume	200
Issue number	3
DOIs	https://doi.org/10.1007/s002200050540
State	Published - 1999

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s002200050540

Fingerprint Dive into the research topics of 'Gerstenhaber algebras and BV-algebras in Poisson geometry'. Together they form a unique fingerprint.

Cite this

@article{fdaaa6a53f8248e49bc3e59b86c57c4d,

title = "Gerstenhaber algebras and BV-algebras in Poisson geometry",

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.",

author = "Ping Xu",

year = "1999",

doi = "10.1007/s002200050540",

language = "English (US)",

volume = "200",

pages = "545--560",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Gerstenhaber algebras and BV-algebras in Poisson geometry

AU - Xu, Ping

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033514096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033514096&partnerID=8YFLogxK

U2 - 10.1007/s002200050540

DO - 10.1007/s002200050540

M3 - Article

AN - SCOPUS:0033514096

VL - 200

SP - 545

EP - 560

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -