On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity

Details On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity

2011-04-09

arxiv.org/abs/1104.1731v4

Mathematics

Operator Algebras

Final version, to appear in Muenster J. Math. A permanence result for the weak approximation property, some corollaries of it

Scientific paper

We first give an overview of the basic theory for discrete unital twisted C*-dynamical systems and their covariant representations on Hilbert C*-modules. After introducing the notion of equivariant representations of such systems and their product with covariant representations, we prove a kind of Fell absorption principle saying that the product of an induced regular equivariant representation with a covariant faithful representation is weakly equivalent to an induced regular covariant representation. This principle is the key to our main result, namely that a certain property, formally weaker than Exel's approximation property, ensures that the system is regular, i.e., the associated full and reduced C*-crossed products are canonically isomorphic.

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