%0 Journal Article
%T Shifted Poisson and Batalin-Vilkovisky structures on the derived variety of complexes
%A Slava Pimenov
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1511.00946v1