POLYNOMIAL IDENTITIES AND AZUMAYA LOCI FOR RATIONAL QUANTUM SPHERES

We prove a number of structure and isomorphism results concerning the noncommutative Natsume–Olsen spheres (formula presented) deformed along a skew- symmetric matrix θ ϵ R. These include (a) the fact that two C-algebras of the form (formula presented)are isomorphic precisely in the obvious cases; (b) the fact that m and n are recoverable from the isomorphism class of (formula presented); (c) the PI character, PI degree and Azumaya loci of (formula presented) for rational θ, along with a realization of their centers as (function algebras of) branched cover of (formula presented); and (d) for rational θ again, the topological finite generation of (formula presented) over their centers, with algebraic finite generation equivalent to being classical (equivalently, Azumaya).