Geodesic
C*-Crossed-Products by an Order-Two Automorphism
Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 37-50

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2010-008-4
Mots-clés : 46L55, 46L80, C*-algebra, C*-crossed-product, fixed point, C*-algebra, action of finite groups, free group, C*-algebras 
Choi, Man-Duen; Latrémolière, Frédéric. C*-Crossed-Products by an Order-Two Automorphism. Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 37-50. doi: 10.4153/CMB-2010-008-4
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