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Shifted Poisson and Batalin-Vilkovisky structures on the derived variety of complexes

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arxiv 1511.00946 v1 pith:LMWW6PVI submitted 2015-11-03 math.AG math.RT

Slava Pimenov This is my paper · ORCID
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keywords structurepoissonshiftedcomplexesderivedvarietyalgebrabatalin-vilkovisky
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We study the shifted Poisson structure on the cochain complex C*(g) of a graded Lie algebra arising from shifted Lie bialgebra structure on g. We apply this to construct a 1-shifted Poisson structures on an infinitesimal quotient of the derived variety of complexes RCom(V) by a subgroup of the automorphisms of V, and a non-shifted Poisson structure on an appropriately defined derived variety of 1-periodic complexes, extending the standard Kirillov-Kostant Poisson structure on gl*_n. We also show that in the case of RCom(V) the 1-shifted structure is up to homotopy a Batalin-Vilkovisky algebra structure.

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  1. Factorization Algebras and Quantum Groups from Generalized Poisson Sigma Models

    hep-th 2026-07 conditional novelty 7.5 of 10

    Generalized Poisson sigma models realize deformation quantizations of holomorphic-topological factorization algebras and produce quantum groups as Koszul duals of their boundary algebras.

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