The dual structure of crossed product C*-algebras with finite groups

TL;DR

This paper characterizes the irreducible representations of crossed product C*-algebras with finite groups by constructing a space of representation pairs and establishing a bijection with the dual algebra, revealing a dual structure.

Contribution

It introduces a novel construction of a representation space for crossed product C*-algebras with finite groups and demonstrates a natural G-action linking it to the algebra's dual.

Findings

The space of irreducible representations is described via pairs of representations.

A natural G-action on the constructed space is established.

The orbit space corresponds bijectively to the dual of the crossed product.

Abstract

We study the space of irreducible representations of a crossed product C*-algebra AxG, where G is a finite group. We construct a space $\Gamma$ which consists of pairs of irreducible representations of A and irreducible projective representations of subgroups of G. We show that there is a natural action of G on $\Gamma$ and that the orbit space G \ $\Gamma$ corresponds bijectively to the dual of AxG.