Automorphisms of crossed products

Crossed Products and Entropy of Automorphisms

Let A be an exact C–algebra, let G be a locally compact group, and let (A, G, α) be a C–dynamical system. Each automorphism αg induces a spatial automorphism Adλg on the reduced crossed product A×α G. In this paper we examine the question, first raised by E. Størmer, of when the topological entropies of αg and Adλg coincide. This had been answered by N. Brown for the particular case of discrete...

Actions and Automorphisms of Crossed Modules

Extension of automorphisms to C*-crossed products with non-trivial centre

Given a quasi-special endomorphism ρ of a C∗ -algebra A with nontrivial center, we study an extension problem for automorphisms of A to a minimal cross-product B of A by ρ . Exploiting some aspects of the underlying generalized Doplicher-Roberts duality theory based on Pimsner algebras, an obstruction to the existence of such extensions is found and described in terms of sections of a suitable ...

Crossed Product Duality for Partial C-automorphisms

For partial automorphisms of C∗-algebras, Takai-Takesaki crossed product duality tends to fail, in proportion to the extent to which the partial automorphism is not an automorphism.

Stable and Real Rank for Crossed Products by Automorphisms with the Tracial Rokhlin Property

We introduce the tracial Rokhlin property for automorphisms of stably finite simple unital C*-algebras containing enough projections. This property is formally weaker than the various Rokhlin properties considered by Herman and Ocneanu, Kishimoto, and Izumi. Our main results are as follows. Let A be a stably finite simple unital C*-algebra, and let α be an automorphism of A which has the tracia...