Selçuk Barlak

Sequentially split ∗-homomorphisms between C*-algebras

We define and examine sequentially split ∗-homomorphisms between C*-algebras and C*-dynamical systems. For a ∗-homomorphism, the property of being sequentially split can be regarded as an approxima...

The spatial Rokhlin property for actions of compact quantum groups

Abstract We introduce the spatial Rokhlin property for actions of coexact compact quantum groups on C ⁎ -algebras, generalizing the Rokhlin property for both actions of classical compact groups and finite quantum groups. Two key ingredients in our approach are the concept of sequentially split ⁎-homomorphisms, and the use of braided tensor products instead of ordinary tensor products. We show that various structure results carry over from the classical theory to this more general setting. In particular, we show that a number of C ⁎ -algebraic properties relevant to the classification program pass from the underlying C ⁎ -algebra of a Rokhlin action to both the crossed product and the fixed point algebra. Towards establishing a classification theory, we show that Rokhlin actions exhibit a rigidity property with respect to approximate unitary equivalence. Regarding duality theory, we introduce the notion of spatial approximate representability for actions of discrete quantum groups. The spatial Rokhlin property for actions of a coexact compact quantum group is shown to be dual to spatial approximate representability for actions of its dual discrete quantum group, and vice versa.

Rokhlin actions of finite groups on UHF-absorbing

This paper serves as a source of examples of Rokhlin actions or locally representable actions of finite groups on C*-algebras satisfying a certain UHF-absorption condition. We show that given any finite group

\mathrm C^∗

G

-algebras

and a separable, unital C*-algebra

The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras

A

Cartan subalgebras and the UCT problem

that absorbs

On diagonal quasi-free automorphisms of simple Cuntz-Krieger algebras.

M_{|G|^\infty}

Mini-Workshop: MASAs and Automorphisms of C*-Algebras

tensorially, one can lift any group homomorphism

Approaching the UCT problem via crossed products of the Razak-Jacelon algebra

G\to\operatorname{Aut}(A)/{\approx_u}