46L57 — 2 articles found.

A classification theorem for certain actions of $\mathbb{R}$ on $C^*$-algebras

C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (1), 2005 pp. 25–32
Vol.27 (1) 2005
Andrew J. Dean Details
(Received: 2004-10-06 )
(Received: 2004-10-06 )

Andrew J. Dean, Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, P7B 5E1; email: andrew.dean@lakeheadu.ca

Abstract/Résumé:

It is shown that two \(C^*\)-dynamical systems of the form \((K\otimes A, \mathbb{R}, \mathrm{Ad} U\otimes id)\), where \(U\) is a unitary representation of \(\mathbb{R}\) that decomposes as a finite direct sum of non-trivial irreducible representations whose multiplicities have greatest common denominator 1, and \(A\) is a simple, unital \(C^*\)-algebra with real rank zero and cancellation, are equivariantly isomorphic if, and only if, the two representations are unitarily equivalent. As a corollary, a classification result for certain inductive limit type actions of \(\mathbb{R}\) on stable UHF algebras is given.

Il est montré que deux systèmes \(C^*\)-dynamiques de la forme \((K\otimes A, \mathbb{R}, \mathrm{Ad} U\otimes id)\)\(U\) est une representation unitaire de \(\mathbb{R}\), qui décompose comme une somme directe et finie des representations non-triviales et irréductibles dont les multiplicités ont 1 comme le dénominateur commun et le plus grand, et \(A\) est un \(C^*\)-algèbre simple, avec l’unité et avec rang réel zéro et annullation, sont isomorphe équivariantement si et seulement si les deux representations sont équivalentes unitairement. Comme un corollaire, un résultat classification pour quelques actions du type de la limite inductive de \(\mathbb{R}\) sur les algèbres d’UHF stables est aussi donné.

Keywords: C∗-dynamical system, classification

AMS Subject Classification: Derivations; dissipations and positive semigroups in $C^*$-algebras 46L57

PDF(click to download): A classification theorem for certain actions of $mathbb{R}$ on $C^*$-algebras

An Invariant for Actions ofℝon UHF C*-algebras

C. R. Math. Rep. Acad. Sci. Canada Vol. 23 (3) 2001, pp. 91–96
Vol.23 (3) 2001
A.J. Dean Details
(Received: 2001-01-22 )
(Received: 2001-01-22 )

A.J. Dean

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Derivations; dissipations and positive semigroups in $C^*$-algebras 46L57

PDF(click to download): An Invariant for Actions of ℝ on UHF C*-algebras

Full Text Pdfs only available for current year and preceding 5 blackout years when accessing from an IP address registered with a subscription. Historical archives earlier than the 5 year blackout window are open access.