Rigidity of quantum algebras

Abstract Given an associative ‐algebra , we call strongly rigid if for any pair of finite subgroups of its automorphism groups , such that , then and must be isomorphic. In this paper, we show that a large class of filtered quantizations are strongly rigid. We also solve the inverse Galois problem for a wide class of rational Cherednik algebras that includes all (simple) classical generalized Weyl algebras, and also for quantum tori. Finally, we show that the Picard group of an ‐dimensional quantum torus is isomorphic to the group of its outer automorphisms.