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• W3159472526 abstract "We study the Poincare duality of smooth Poisson manifolds, and show that, if the modular symmetry is semisimple, that is, the modular vector is diagonalizable, there is a mixed complex associated to the Poisson complex which, combining with the twisted Poincare duality, gives a Batalin-Vilkovisky algebra structure on the Poisson cohomology, and a gravity algebra structure on the negative cyclic Poisson homology. This generalizes the previous results obtained by Xu et al for unimodular Poisson algebras. We also show that these two algebraic structures are preserved under Kontsevich's deformation quantization, and in the case of polynomial algebras they are also preserved by Koszul duality." @default.
• W3159472526 created "2021-05-10" @default.
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• W3159472526 date "2021-04-29" @default.
• W3159472526 modified "2023-09-24" @default.
• W3159472526 title "Batalin-Vilkovisky and gravity algebras on Poisson manifolds with semisimple modular symmetry" @default.
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