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

By R. Exel, Anatoly M. Vershik. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2002

87 citations recorded by the source corpus.

Abstract 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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4685214acf00294573e55e1582dedfd48e909848

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In Algebra and Number Theory

1. Aidan Sims
2. L. O. Clark
3. J. Brown
4. Cynthia Farthing
5. Ben Steinberg
6. Trent Yeend
7. R. Exel
8. Enrique Pardo

In Mathematical Physics

1. Aidan Sims
2. L. O. Clark
3. J. Brown
4. Cynthia Farthing
5. Ben Steinberg
6. Trent Yeend
7. R. Exel
8. Enrique Pardo

Citations in the corpus

• Simplicity of algebras associated to étale groupoids (2012, methodology): “incipal, we went looking for examples — other than k-graph groupoids — of ´etale groupoids with totally disconnected unit spaces to test the hypothesis. We were led to the work of Exel and Vershik in [11]. Their characterisation of simplicity [11, Theorem 11.2] led us to condition (3) of Lemma 3.1 a”