Prime and Primitive Ideals of a Class of Iterated Skew Polynomial Rings

Abstract

Hodges and Levasseur described the primitive spectra of quantized coordinate rings of SL3 [14], and then of SLn [15]. These results established a close connection between primitive ideals, torus action, and Poisson geometry. The proofs relied on explicit computations involving generators and relations. Subsequently, Joseph generalized the Hodges–Levasseur program to semisimple algebraic quantum groups [17]. Hodges et al. then expanded Joseph’s work to include certain multiparameter deformations [16]. These papers rely less on concrete calculations and more on deeper, more conceptual, techniques. It is a natural and important question, then, as to how the preceding theory might apply to other algebras, particularly other algebras arising in the study of quantum groups. Goodearl and Letzter established parallel results for certain iterated skew polynomial rings [13], with application to quantum Weyl algebras and to some quantum coordinate rings.