Poisson structures on C[X1; : : : ;Xn] associated with rigid Lie algebras

Abstract

We present the classical Poisson-Lichnerowicz cohomology for the Poisson algebra of polynomials C[X 1 , . . . , X n ] using exterior calculus. After presenting some non-homogenous Poisson brackets on this algebra, we compute Poisson cohomological spaces when the Poisson structure corresponds to a bracket of a rigid Lie algebra. MSC: 17B-XX