Mathematical Reports - Comptes rendus mathématiques

of the Academy of Science | de l'Académie des sciences

  • Home
  • Articles
  • News
  • Editorial Board
  • General Information
    • General Information
    • Preparation of Manuscripts
    • Subscription Information
    • FAQ
    • Help

April 10, 2015 By

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

March 30, 2005

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 \((K\otimes A, \mathbb{R}, \mathrm{Ad} U\otimes id)\) où \(U\) 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

[This journal is open access except for the current year and the preceding 5 years]

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

Filed Under: Uncategorized

 Volume / Issue

Most used Keywords

algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

Be notified of new issues

Copyright © 2023 · The Royal Society of Canada | La Société royale du Canada · Log in
ISSN: 2816-5810 (Online)