Frobenius Poisson algebras

doi:10.1007/s11464-019-0756-x

Front. Math. China

2019, Vol. 14

Issue (2) : 395-420 https://doi.org/10.1007/s11464-019-0756-x

RESEARCH ARTICLE

Frobenius Poisson algebras

Juan LUO¹(

), Shengqiang WANG², Quanshui WU³

¹. Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
². Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
³. School of Mathematical Sciences, Fudan University, Shanghai 200433, China

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Abstract

This paper is devoted to study Frobenius Poisson algebras. We introduce pseudo-unimodular Poisson algebras by generalizing unimodular Poisson algebras, and investigate Batalin-Vilkovisky structures on their cohomology algebras. For any Frobenius Poisson algebra, all Batalin-Vilkovisky operators on its Poisson cochain complex are described explicitly. It is proved that there exists a Batalin-Vilkovisky operator on its cohomology algebra which is induced from a Batalin-Vilkovisky operator on the Poisson cochain complex, if and only if the Poisson structure is pseudo-unimodular. The relation between modular derivations of polynomial Poisson algebras and those of their truncated Poisson algebras is also described in some cases.

Keywords Poisson algebra Frobenius algebra Batalin-Vilkovisky algebra Poisson (co)homology modular derivation

Corresponding Author(s): Juan LUO

Issue Date: 14 May 2019

Cite this article:

Juan LUO,Shengqiang WANG,Quanshui WU. Frobenius Poisson algebras[J]. Front. Math. China, 2019, 14(2): 395-420.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0756-x
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I2/395

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