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We study the shifted Poisson structure on the cochain complex C*(g) of agraded Lie algebra arising from shifted Lie bialgebra structure on g. We applythis to construct a 1-shifted Poisson structures on an infinitesimal quotientof the derived variety of complexes RCom(V) by a subgroup of the automorphismsof V, and a non-shifted Poisson structure on an appropriately defined derivedvariety of 1-periodic complexes, extending the standard Kirillov-KostantPoisson structure on gl*_n. We also show that in the case of RCom(V) the1-shifted structure is up to homotopy a Batalin-Vilkovisky algebra structure.

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