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On (co)homology of Frobenius Poisson algebras

Published online by Cambridge University Press:  05 September 2014

Can Zhu ,
Fred Van Oystaeyen  and
Yinhuo Zhang
Can Zhu
Affiliation:
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China, czhu@usst.edu.cn Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium
Fred Van Oystaeyen
Affiliation:
Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium, fred.vanoystaeyen@ua.ac.be
Yinhuo Zhang
Affiliation:
Department Mathematics and Statistics, University of Hasselt, Universitaire Campus, 3590 Diepeenbeek, Belgium, yinhuo.zhang@uhasselt.be
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Abstract

In this paper, we study Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between Poisson homology and Poisson cohomology of Frobenius Poisson algebras, similar to that between Hochschild homology and Hochschild cohomology of Frobenius algebras. Then we use the non-degenerate bilinear form on a unimodular Frobenius Poisson algebra to construct a Batalin-Vilkovisky structure on the Poisson cohomology ring making it into a Batalin-Vilkovisky algebra.

Keywords

Poisson algebraFrobenius algebraPoisson (co)homologydualityBV algebraPrimary 17B6317B3516E40
Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 2 , October 2014 , pp. 371 - 386
Copyright
Copyright © ISOPP 2014 

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