JournalsjncgVol. 15, No. 3pp. 889–918

Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras

  • Xiaojun Chen

    Sichuan University, Chengdu, China

  • Youming Chen

    Chongqing University of Technology, China

  • Farkhod Eshmatov

    Uzbekistan Academy of Sciences and AKFA University, Tashkent, Uzbekistan

  • Song 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