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

2015/11/03 by Slava Pimenov, Pimenov, Slava
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1511.00946

openalex publication_date 2015/11/03 · openalex created_date 2022/09/13 · openalex updated_date 2026/07/28

Abstract

We study the shifted Poisson structure on the cochain complex C*(g) of a\ngraded Lie algebra arising from shifted Lie bialgebra structure on g. We apply\nthis to construct a 1-shifted Poisson structures on an infinitesimal quotient\nof the derived variety of complexes RCom(V) by a subgroup of the automorphisms\nof V, and a non-shifted Poisson structure on an appropriately defined derived\nvariety of 1-periodic complexes, extending the standard Kirillov-Kostant\nPoisson structure on gl*_n. We also show that in the case of RCom(V) the\n1-shifted structure is up to homotopy a Batalin-Vilkovisky algebra structure.\n

Citations

• Derived varieties of complexes and Kostant's theorem for gl(m|n)
• Batalin-Vilkovisky algebras and cyclic cohomology of Hopf algebras
• Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson\n bialgebroids

Related

• Shifted symplectic and Poisson structures on global quotients
• Shifted double Poisson structures and noncommutative Poisson extensions
• Shifted bisymplectic and double Poisson structures on non-commutative derived prestacks
• Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry
• Shifted Poisson structures on higher Chevalley-Eilenberg algebras