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

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DOI

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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     author = {Choi, Man-Duen and Latr\'emoli\`ere, Fr\'ed\'eric},
     title = {C*-Crossed-Products by an {Order-Two} {Automorphism}},
     journal = {Canadian mathematical bulletin},
     pages = {37--50},
     year = {2010},
     volume = {53},
     number = {1},
     doi = {10.4153/CMB-2010-008-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-008-4/}
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