文献类型：期刊文献

英文题名：Twisted duality and BV-algebras on the (co)homology of quadratic Poisson structures

作者：Li, Yaxuan[1];Wang, Shengqiang[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2026

卷号：108

期号：1-2

起止页码：163

外文期刊名：PUBLICATIONES MATHEMATICAE DEBRECEN

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001697964000008)】；

基金：This work is supported by the Undergraduate Training Program on Innovation and Entrepreneurship Grant X20243, and the National Natural Science Foundation of China No. 11771085.

语种：英文

外文关键词：Poisson algebra; Poisson cohomology; modular derivation; Koszul dual; Batalin-Vilkovisky algebra

摘要：This paper is devoted to the calculation of Poisson (co)homologies for polynomial Poisson algebras in two variables and their Koszul dual Poisson algebras. According to the computation results, the twisted Poincare dualities were recovered via modular derivations. Moreover, the relations between the modular derivations of polynomial Poisson algebras and their Koszul dual Poisson algebras were given explicitly. Finally, we also investigate the existence of Batalin-Vilkovisky algebra structures on their Poisson cohomology groups.