Poisson structures on C[X1, . . . , Xn] associated with rigid Lie algebras

Nicolas GOZE

Abstract

We present the classical Poisson-Lichnerowicz cohomology for the Poisson algebra of polynomials C[X1; : : : ;Xn] 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