Frontiers of Mathematics in China >
Frobenius Poisson algebras
Received date: 08 Oct 2018
Accepted date: 18 Feb 2019
Published date: 15 Apr 2019
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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.
Juan LUO , Shengqiang WANG , Quanshui WU . Frobenius Poisson algebras[J]. Frontiers of Mathematics in China, 2019 , 14(2) : 395 -420 . DOI: 10.1007/s11464-019-0756-x
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