Operator Algebra Seminar

Speaker: Selcük Barlak, Münster

Title: Rokhlin actions of finite groups on UHF-absorbing C*-algebras

Abstract: In this talk we show the existence of various Rokhlin actions of finite groups on separable, unital, UHF-absorbing C*-algebras. Given a finite group G and a family of automorphisms indexed by G that defines a G-action up to approximate unitary equivalence, there exists a Rokhlin action representing this family up to pointwise approximate unitary equivalence. We use this to conclude that for a UHF-absorbing C*-algebra in the UCT class which is either a Kirchberg algebra or simple, nuclear and TAF, every G-action on the (ordered) K-theory lifts to a Rokhlin action. As an application, we recover and extend Blackadar's famous construction of symmetries on the CAR algebra yielding fixed point algebras with non-trivial K₁-groups. This arises as a combination of the main results of this talk and Lin's classification of simple, nuclear TAF algebras. This is joint work with Gábor Szabó.