Article

Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras

Xiaojun ChenSichuan University, Chengdu, ChinaYouming ChenChongqing University of Technology, ChinaFarkhod EshmatovUzbekistan Academy of Sciences and AKFA University, Tashkent, UzbekistanSong YangTianjin University, China

Journal of Noncommutative Geometryjournal2021en

ABI

Abstract

We study the noncommutative Poincaré duality between the Poisson homology and cohomology of unimodular Poisson algebras, and show that Kontsevich’s deformation quantization as well as Koszul duality preserve the corresponding Poincaré duality. As a corollary, the Batalin– Vilkovisky algebra structures that naturally arise in these cases are all isomorphic.

Topics

Advanced Topics in Algebra Algebraic structures and combinatorial models Homotopy and Cohomology in Algebraic Topology

Identifiers

DOI: 10.4171/jncg/425

Citations and references

Cited by 00 references

Metrics — AkademScholar · Coming soon