Induced Representations of Twisted C*-dynamical Systems

A Note On Morita Equivalence of TwistedC * - Dynamical

We present an elementary proof that every twisted C*-dynamical system is Morita equivalent to an ordinary system. As a corollary we prove the equivalence C0(G=H; A) ~ ;~ u G A ;u H for Busby-Smith twisted dynamical systems, generalizing an important result of Green. It is essentially the content of a recent theorem of Echterhoo 5, Theorem 1] that every twisted dynamical system is Morita equival...

Realization of minimal C*-dynamical systems in terms of Cuntz-Pimsner algebras

In the present paper we study tensor C*-categories with non-simple unit realised as C*dynamical systems (F ,G, β) with a compact (non-Abelian) group G and fixed point algebra A := F . We consider C*-dynamical systems with minimal relative commutant of A in F , i.e. A∩F = Z, where Z is the center of A which we assume to be nontrivial. We give first several constructions of minimal C*-dynamical s...

Dynamical Systems on Hilbert C*-Modules

Dilations for $C^ast$-dynamical systems with abelian groups on Hilbert $C^ast$-modules

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

Naturality and Induced Representations

We show that induction of covariant representations for C∗-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of C∗-algebras and dynamical systems, and extending the usual constructions of crossed products to define the appropriate functors. From this point of view, Green’s Impri...