${{C}^{*}}$ -Algebras of Irreversible Dynamical Systems

Exel, R. ; Vershik, A.

Canadian journal of mathematics, Tome 58 (2006) no. 1, pp. 39-63

Résumé

We show that certain ${{C}^{*}}$ -algebras which have been studied by, among others, Arzumanian, Vershik, Deaconu, and Renault, in connection with a measure-preserving transformation of a measure space or a covering map of a compact space, are special cases of the endomorphism crossed product construction recently introduced by the first named author. As a consequence these algebras are given presentations in terms of generators and relations. These results come as a consequence of a general theorem on faithfulness of representations which are covariant with respect to certain circle actions. For the case of topologically free covering maps we prove a stronger result on faithfulness of representations which needs no covariance. We also give a necessary and sufficient condition for simplicity.

Détail

DOI : 10.4153/CJM-2006-003-x

Mots-clés : 46L55, 37A55

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