Noncommutative topological dynamics and compact actions on C∗-algebras

Actions of Hopf algebras on noncommutative algebras

Often A is called H-module algebra. We refer reader to [11, 6] for the basic information concerning Hopf algebras and their actions on associative algebras. Definition 1.2 The invariants of H in A is the set AH of those a ∈ A, that ha = ε(h)a for each h ∈ H. Straightforward computations show, that AH is subalgebra of A. The notion of action of Hopf algebra on associative algebra generalize the ...

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.

APPROXIMATELY INNER sigma-DYNAMICS ON C* ALGEBRAS

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

C∗-algebras and topological dynamics: finite approximation and paradoxicality

Contents Chapter 1. Introduction 5 Chapter 2. Internal measure-theoretic phenomena 13 1. Amenable groups and nuclearity 13 2. Amenable actions, nuclearity, and exactness 16 3. The type semigroup, invariant measures, and pure infiniteness 21 4. The universal minimal system 29 5. Minimal actions, pure infiniteness, and nuclearity 31 Chapter 3. External measure-theoretic phenomena 33 1. Sofic grou...