Crossed module actions on continuous trace C*-algebras

Pennig Ulrich, Meyer Ralf

Abstract

We lift an action of a torus T^n on the spectrum of a continuous trace algebra to an action of a certain crossed module of Lie groups that is an extension of R^n. We compute equivariant Brauer and Picard groups for this crossed module and describe the obstruction to the existence of an action of R^n in our framework.