Crossed products of continuous-trace 𝐶*-algebras by smooth actions

Abstract

We study in detail the structure of C ∗ {C^{\ast }} -crossed products of the form A ⋊ α G A \rtimes {}_\alpha G , where A A is a continuous-trace algebra and α \alpha is an action of a locally compact abelian group G G on A A , especially in the case where the action of G G on A ^ \hat A has a Hausdorff quotient and only one orbit type. Under mild conditions, the crossed product has continuous trace, and we are often able to compute its spectrum and Dixmier-Douady class. The formulae for these are remarkably interesting even when G G is the real line.