Deformation of Fell bundles

Abstract

In this paper we study deformations of $C^*$-algebras that are given as cross-sectional $C^*$-algebras of Fell bundles over locally compact groups $G$. Our deformation comes from a direct deformation of the Fell bundles via certain parameters, like automorphisms of the Fell bundle, group cocycles, or central group extensions of $G$ by the circle group $\mathbb{T}$, and then taking cross-sectional algebras of the deformed Fell bundles. We then show that this direct deformation method is equivalent to the deformation via the dual coactions by similar parameters as studied previously in [4,7].