Irreducible Induced Representations of Fell Bundle C*-Algebras

TL;DR

This paper establishes conditions for when irreducible representations of stability groups induce irreducibly in Fell bundle C*-algebras, broadening previous results and impacting various dynamical system constructions.

Contribution

It generalizes earlier work by providing precise criteria for irreducibility induction in Fell bundle C*-algebras, encompassing many dynamical system examples.

Findings

Provides necessary and sufficient conditions for irreducible induction.

Generalizes previous results by Echterhoff and the second author.

Applies to a wide range of C*-algebras from dynamical systems.

Abstract

We give precise conditions under which irreducible representations associated to stability groups induce to irreducible representations for Fell bundle C*-algebras. This result generalizes an earlier result of Echterhoff and the second author. Because the Fell bundle construction subsumes most other examples of C*-algebras constructed from dynamical systems, our result percolates down to many different constructions including the many flavors of groupoid crossed products.