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

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

2011-04-10

arxiv.org/abs/1104.1810v2

Mathematics

Operator Algebras

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

Scientific paper

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.

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