First we recall the notions of Poisson algebras and Poisson(co)homology.Second we introduce the notion of differential KS structure and show that Poisson cohomology complex together with Poisson homology complex form a differential KS structure.Last based on the work of N.Nakanishi,we determine the Gerstenhaber algebra structure over the Poisson cohomology of plane quadratic Poisson structures,and as a consequence,the Poisson coho-mology of the elliptic and hyperbolic structures are isomorphic as Gerstenhaber algebras. |