Shifted Poisson and Batalin-Vilkovisky structures on the derived variety of complexes
Algebraic Geometry
2015-11-04 v1 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1511.00946,
title = {Shifted Poisson and Batalin-Vilkovisky structures on the derived variety of complexes},
author = {Slava Pimenov},
journal= {arXiv preprint arXiv:1511.00946},
year = {2015}
}