POISSON STRUCTURES DUE TO LIE-ALGEBRA REPRESENTATIONS

Using a unitary solution of the classical Yang-Baxter equation on a Li e algebra g we describe a particular way of constructing homogeneous q uadratic Poisson structures on the dual of a g-module V and study some local features of the symplectic foliation due to the involutive dist ribution of the Hamiltonian vector fields. We also give some examples where the symplectic leaves are explicitly calculated.