Covariant Representations of C*-algebras and their Compact Automorphism Groups

Firuz Kamalov

Covariant Representations of C*-algebras and their Compact Automorphism Groups

Operator Algebras 2011-04-13 v2

Authors: Firuz Kamalov

Abstract

Let G be a compact group. Let (X,G) be a standard Borel G-measure space. We show that the group action on (X, G) is transitive if and only if it is ergodic. Using this result, we show that every irreducible covariant representation of a C*-dynamical system (A, G) is induced from a stability group. In addition, we show that (A, G) satisfies strong-EHI.

Keywords

covariant representations C*-algebras compact automorphism groups ergodic action transitive action C*-dynamical system strong-EHI

Cite

@article{arxiv.1104.1810,
  title  = {Covariant Representations of C*-algebras and their Compact Automorphism Groups},
  author = {Firuz Kamalov},
  journal= {arXiv preprint arXiv:1104.1810},
  year   = {2011}
}

Comments

14 pages. Minor typos are corrected, Proposition 7 is changed to Corollary 7, and the proof of Theorem 8 is slightly modified

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