Crossed module actions on continuous trace $C^{\ast }$-algebras

Abstract

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

27 pages, added background material about T-Duality, added references, extended section about non-associative C*-algebras

References in corpus (2)

• On the Topology and Flux of T-Dual Manifolds
• Topology and Flux of T-Dual Manifolds with Circle Actions