On generalized Abelian deformations

Abstract

We study sun-products on $\R^n$, i.e. generalized Abelian deformations associated with star-products for general Poisson structures on $\R^n$. We show that their cochains are given by differential operators. As a consequence, the weak triviality of sun-products is established and we show that strong equivalence classes are quite small. When the Poisson structure is linear (i.e., on the dual of a Lie algebra), we show that the differentiability of sun-products implies that covariant star-products on the dual of any Lie algebra are equivalent each other.