## Mathematics, Department of

#### First Advisor

Allan Donsig

#### Date of this Version

Summer 7-18-2011

#### Abstract

Given a C*-dynamical system (A, G, σ) the crossed product C*-algebra A x _{σ}G encodes the action of G on A. By the universal property of A x _{σ}G 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 _{σ}G. Therefore, the study of representations of A x _{σ}G 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, G_{0}, σ) where π_{0} 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 _{σ}G 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

## 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