Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras

Xiaojun Chen; Youming Chen; Farkhod Eshmatov; Song Yang

doi:10.4171/jncg/425

JournalsjncgVol. 15, No. 3pp. 889–918

Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras

Xiaojun Chen
Sichuan University, Chengdu, China
- MathSciNet
- zbMATH Open
Youming Chen
Chongqing University of Technology, China
- MathSciNet
Farkhod Eshmatov
Uzbekistan Academy of Sciences and AKFA University, Tashkent, Uzbekistan
- MathSciNet
- zbMATH Open
Song Yang
Tianjin University, China
- MathSciNet
- zbMATH Open

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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.

Cite this article

Xiaojun Chen, Youming Chen, Farkhod Eshmatov, Song Yang, Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras. J. Noncommut. Geom. 15 (2021), no. 3, pp. 889–918

DOI 10.4171/JNCG/425