Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras
Xiaojun Chen
Sichuan University, Chengdu, ChinaYouming Chen
Chongqing University of Technology, ChinaFarkhod Eshmatov
Uzbekistan Academy of Sciences and AKFA University, Tashkent, UzbekistanSong Yang
Tianjin University, China
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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