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Covariant representations of C*-dynamical systems involving compact groups

Firuz Kamalov, University of Nebraska - Lincoln

Abstract

Given a C*-dynamical system (A, G, σ) the crossed product C*-algebra A×σG encodes the action of G on A. By the universal property of A ×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 σG. Therefore, the study of representations of A ×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,G0, σ) where π0 is a factor representation. This extends a result obtained in [3] for finite groups. It was shown in [10] that if G is an amenable group then every primitive ideal of A ×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 in [5]. ^

Subject Area

Mathematics

Recommended Citation

Kamalov, Firuz, "Covariant representations of C*-dynamical systems involving compact groups" (2011). ETD collection for University of Nebraska - Lincoln. AAI3465903.
http://digitalcommons.unl.edu/dissertations/AAI3465903

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