CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

$C^*$-Crossed-Products by an Order-Two Automorphism

  Published:2009-12-04
 Printed: Mar 2010
  • Man-Duen Choi
  • Frédéric Latrémolière
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax  

Abstract

We describe the representation theory of $C^*$-crossed-products of a unital $C^*$-algebra A by the cyclic group of order~2. We prove that there are two main types of irreducible representations for the crossed-product: those whose restriction to A is irreducible and those who are the sum of two unitarily unequivalent representations of~A. We characterize each class in term of the restriction of the representations to the fixed point $C^*$-subalgebra of~A. We apply our results to compute the K-theory of several crossed-products of the free group on two generators.
MSC Classifications: 46L55, 46L80 show english descriptions Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
46L55 - Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
46L80 - $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/