文献类型：期刊文献

英文题名：Poincaré duality for smooth Poisson algebras and BV structure on Poisson cohomology

作者：Luo, J.[1];Wang, S. -Q.[2];Wu, Q. -S.[3]

机构：[1]Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[3]Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

年份：2024

卷号：649

起止页码：169

外文期刊名：JOURNAL OF ALGEBRA

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001226328600001)】；

基金：J. Luo is supported by the NSFC (Grant No. 11901396) . S. -Q. Wang is supported by the NSFC (Grant No. 11771085) . Q. -S. Wu is supported by the National Key Research and Development Program of China (Grant No. 2020YFA0713200) and NSFC (Grant No. 11771085) .

语种：英文

外文关键词：Poisson algebra; Smooth algebra; Modular derivation; Poincar & eacute; duality; Batalin-Vilkovisky algebra

摘要：Similar to the modular vector fields in Poisson geometry, modular derivations are defined for smooth Poisson algebras with trivial canonical bundle. By twisting Poisson module with the modular derivation, the Poisson cochain complex with values in any Poisson module is proved to be isomorphic to the Poisson chain complex with values in the corresponding twisted Poisson module. Then a version of twisted Poincar & eacute; duality is proved between the Poisson homologies and cohomologies. Furthermore, a notion of pseudo-unimodular Poisson structure is defined. It is proved that the Poisson cohomology as a Gerstenhaber algebra admits a Batalin-Vilkovisky operator inherited from some one of its Poisson cochain complex if and only if the Poisson structure is pseudo-unimodular. This generalizes the geometric version due to P. Xu. The modular derivation and Batalin-Vilkovisky operator are also described by using the dual basis of the K & auml;hler differential module. (c) 2024 Elsevier Inc. All rights reserved.