Isomorphism problems and groups of automorphisms for generalized Weyl algebras

Abstract

We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities and the algebras similar to U ( s l 2 ) U(\mathfrak {sl}_2) introduced by S. P. Smith. For the former, we generalize results of Dixmier on the first Weyl algebra and the minimal primitive factors of U ( s l 2 ) U(\mathfrak {sl}_2) by finding sets of generators for the group of automorphisms.