Completeness of the isomorphism problem for separable C*-algebras

Abstract

This paper studies the descriptive set-theoretical complexity of the isomorphism problem for separable C*-algebras. We prove that the isomorphism problem for separable (simple, AI) C*-algebras is complete in the class of orbit equivalence relations. This means that any isomorphism problem arising from a continuous action of a separable completely metrizable group can be reduced to the isomorphism of simple, separable AI C*-algebras.