| Title | On the Exel Crossed Product of Topological Covering Maps |
| Authors | Toke Meier Carlsen, Sergei Silvestrov |
| Alternative Location | http://dx.doi.org/10.1007/s..., Restricted Access |
| Publication | Acta Applicandae Mathematicae |
| Year | 2009 |
| Volume | 108 |
| Issue | 3 |
| Pages | 573 - 583 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Springer Netherlands |
| Abstract English | For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product C (*)-algebras C(X)a < S (alpha,a"')a"center dot introduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering map is topologically free; the canonical embedding of C(X) into C(X)a < S (alpha,a"')a"center dot is a maximal abelian C (*)-subalgebra of C(X)a < S (alpha,a"')a"center dot; any nontrivial two sided ideal of C(X)a < S (alpha,a"')a"center dot has non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)a < S (alpha,a"')a"center dot is faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product C (*)-algebras of homeomorphism dynamical systems. |
| Keywords | Crossed product algebra, Topologically free dynamical, system, Ideals, Maximal abelian subalgebra, Covering map, |
| ISBN/ISSN/Other | ISSN: 0167-8019 |
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