Representations of some PI algebras

In this paper we find the degree of quantizations of Weyl algebras. Moreover in some cases we describe representations of maximal degree. For the quantized Weyl algebras, we prove that certain nice localizations are quasipolynornial algebras. Finally we use the general result to get the centers of the various algebras hence generalizing and reproving results from Awami et al. (1988) and Morikawa (1989). Essential for many of our results is a description of the simple R[Theta; alpha]-modules in terms of the k-automorphism alpha and the simple R-modules, here R is a prime affine PI algebra, k an algebraically closed field of characteristic 0 and alpha a k-automorphism of finite order.