The Fourier-Stieltjes algebra of a C*-dynamical system II

TL;DR

This paper extends the study of Fourier-Stieltjes algebras for twisted C*-dynamical systems, exploring how algebraic notions of equivalence reflect system properties and demonstrating amenability preservation under Morita equivalence.

Contribution

It advances understanding of the algebraic structure of twisted C*-dynamical systems and shows amenability is invariant under Morita equivalence.

Findings

Amenability is preserved under Morita equivalence.

Algebra-level notions reflect system equivalences.

Extended the framework for Fourier-Stieltjes algebras in twisted systems.

Abstract

We continue our study of the Fourier-Stieltjes algebra associated to a twisted (unital, discrete) C*-dynamical system and discuss how the various notions of equivalence of such systems are reflected at the algebra-level. As an application, we show that the amenability of a system, as defined in our previous work, is preserved under Morita equivalence.