### 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 | |

State | Published - Jan 1 1999 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Communications In Mathematical Physics*, vol. 200, no. 3, pp. 545-560. https://doi.org/10.1007/s002200050540

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Gerstenhaber algebras and BV-algebras in Poisson geometry

AU - Xu, Ping

PY - 1999/1/1

Y1 - 1999/1/1

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 -