2002/03/19 by R. Exel, Exel, R., A. M. Vershik +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics #math.DS #math.OA
paper · pdf · doi:10.48550/arxiv.math/0203185
Plain Tex, 19 pages
arxiv created 2002/03/19 · openalex publication_date 2002/03/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to 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.