Gerstenhaber Algebras and BV-Algebras in Poisson Geometry
Gerstenhaber Algebras and BV-Algebras in Poisson Geometry
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DOI：
10.1007/s002200050540
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发表时间：
1997-03
影响因子：
2.4
通讯作者：
P. Xu
中科院分区：
文献类型：
--
作者：
P. Xu
本文的目的是利用Gerstenhaber代数和bv代数等代数结构，建立向量束上各种几何结构之间的显式对应关系。讨论了一些应用。特别地，我们发现了Koszul-Brylinski算子与泊松流形的模类之间的显式联系。因此，我们证明了非模泊松结构的泊松同构与泊松上同构。
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.