Actions of compact quantum groups 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.

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.

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

reiter’s properties for the actions of locally compact quantum goups on von neumann algebras

Reiter’s Properties for the Actions of Locally Compact Quantum Groups on Von Neumann Algebras

The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter’s conditions for such an action are discussed. Several applications to some specific actions related to certain representations and corepresentaions are presented.