Covariant Representations of C*-dynamical systems Involving Compact Groups

Authors

Firuz Kamalov, University of Nebraska-LincolnFollow

First Advisor

Allan Donsig

Date of this Version

Summer 7-18-2011

Document Type

Article

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Allan Donsig. Lincoln, Nebraska: August, 2011

Copyright 2011 Firuz Kamalov

Abstract

Given a C*-dynamical system (A, G, σ) the crossed product C*-algebra A x _σG encodes the action of G on A. By the universal property of A x _σG there exists a one to one correspondence between the set all covariant representations of the system (A, G, σ) and the set of all *-representations of A x _σG. Therefore, the study of representations of A x _σG is equivalent to that of covariant representations of (A, G, σ).

We study induced covariant representations of systems involving compact groups. We prove that every irreducible (resp. factor) covariant representation of (A, G, σ) is induced from an irreducible (resp. factor) representation of a subsystem (A, G₀, σ) where π₀ is a factor representation. This extends a result obtained by Arias and Latremoliere for finite groups. It was shown by Gootman and Rosenberg, that if G is an amenable group then every primitive ideal of A x _σG is induced from a stability group. If G is compact then we obtain a stronger result, that is, every irreducible representation of (A, G, σ) is induced from a stability group. In addition, we show that (A, G, σ) satisfies the strong-EHI property introduced by Echterhoff and Williams.

Adviser: Allan Donsig