Algebraic isomorphisms of quantized homogeneous spaces

Abstract

We describe a proof of the following folklore theorem: If $\cX = G/K$ is the homogeneous space of a simply connected compact semisimple Lie group with Poisson-Lie stabilizers, then the $q$-deformed algebras of regular functions $\CC[\cX_q]$ with $0<q\le 1$ are mutually non-isomorphic as $\ast$-algebras.