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
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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 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 -