文献类型：期刊文献

英文题名：Batalin-Vilkovisky structures on the cohomologies of tensor Poisson algebras

作者：Luo, J.[1];Wang, S. -Q[2]

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

年份：2025

卷号：39

期号：9

起止页码：2913

外文期刊名：FILOMAT

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001470414100007)】；

基金：We would like to thank the anonymous referees for their valuable comments and suggestions that led to the improvement of the manuscript. J. Luo is supported by the NSFC (Grant No. 11901396) . S.-Q. Wang is supported by the NSFC (Grant No. 11771085) .

语种：英文

外文关键词：Poisson algebra; tensor product; Batalin-Vilkovisky algebra; smooth algebra; Frobenius algebra

摘要：It has been proved that the Poisson cohomology ring of a Poisson algebra has a BatalinVilkovisky algebra structure iff the Poisson algebra is pseudo-unimodular. In this paper, it is proved that the tensor algebra of two pseudo-unimodular Poisson algebras is also pseudo-unimodular, thus its Poisson cohomology ring is still a Batalin-Vilkovisky algebra. Furthermore, This Batalin-Vilkovisky algebra is isomorphic to the tensor Batalin-Vilkovisky algebra of the respective Poisson cohomology rings of the two pseudo-unimodular Poisson algebras.