Graded Poisson Lie structures on classical complex Lie groups

The external algebra over holomorphic first order differential forms on a complex Lie groupG is endowed with the structure of a graded Poisson Lie algebra. This structure is introduced via graded bicovariant brackets that are shown to be in one to one correspondence withG-invariant tensors of special symmetry. Complete classification of graded Poisson Lie structures defined by homogeneous brackets is obtained for the case of classical complex Lie groups.