Model theory and Rokhlin dimension for compact quantum group actions

The Abramov–rokhlin Entropy Addition Formula for Amenable Group Actions

In this note we show that the entropy of a skew product action of a countable amenable group satisfies the classical formula of Abramov and Rokhlin.

Compact Group Actions That Raise Dimension to Infinity

Interest in group actions with the property that the orbit space has greater dimension than the original space is motivated in part by P. A. Smith’s generalization [S2] of Hilbert’s Fifth Problem [H]. Hilbert asked whether a topological group G the underlying space of which, |G|, is a (finitedimensional) manifold admits the structure of a Lie group, i.e., whether |G| admits the structure of a r...

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

Finite Cyclic Group Actions with the Tracial Rokhlin Property

We give examples of actions of Z/2Z on AF algebras and AT algebras which demonstrate the differences between the (strict) Rokhlin property and the tracial Rokhlin property, and between (strict) approximate representability and tracial approximate representability. Specific results include the following. We determine exactly when a product type action of Z/2Z on a UHF algebra has the tracial Rok...