  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.
