Compact actions on C*-algebras

Compact Quantum Group Actions on C*-algebras and Invariant Derivations

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Proper Actions of Groupoids on C-algebras

This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid dynamical system extends both the notion of proper actions of groups on topological spaces and the notion of the proper group dynamical systems introduced...

Part III, Free Actions of Compact Quantum Groups on C∗-Algebras

We study and classify free actions of compact quantum groups on unital C∗algebras in terms of generalized factor systems. Moreover, we use these factor systems to show that all finite coverings of irrational rotation C∗-algebras are cleft.

Index Theory for Actions of Compact Lie Groups on C-algebras

We study the index theory for actions of compact Lie groups on C∗-algebras with an emphasis on principal actions. Given an invariant semifinite faithful trace on the C-algebra we obtain semifinite spectral triples. For circle actions we consider the relation to the dual Pimsner-Voiculescu sequence. On the way we show that the notions “saturated” and “principal” are equivalent for actions by com...