On the Exel Crossed Product of Topological Covering Maps
(2009) In Acta Applicandae Mathematicae 108(3). p.573583 Abstract
 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 noninvertible 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;... (More)
 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 noninvertible 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 nonzero 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 noninvertible dynamics of the corresponding results for crossed product C (*)algebras of homeomorphism dynamical systems. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1518585
 author
 Meier Carlsen, Toke and Silvestrov, Sergei ^{LU}
 organization
 publishing date
 2009
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Crossed product algebra, Topologically free dynamical, system, Ideals, Maximal abelian subalgebra, Covering map
 in
 Acta Applicandae Mathematicae
 volume
 108
 issue
 3
 pages
 573  583
 publisher
 Springer
 external identifiers

 wos:000271941500008
 scopus:71449107536
 ISSN
 01678019
 DOI
 10.1007/s1044000893726
 language
 English
 LU publication?
 yes
 id
 ecfae9057bfe4869a416897878dc1890 (old id 1518585)
 date added to LUP
 20091228 15:15:44
 date last changed
 20180107 06:36:59
@article{ecfae9057bfe4869a416897878dc1890, abstract = {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 noninvertible 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 nonzero 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 noninvertible dynamics of the corresponding results for crossed product C (*)algebras of homeomorphism dynamical systems.}, author = {Meier Carlsen, Toke and Silvestrov, Sergei}, issn = {01678019}, keyword = {Crossed product algebra,Topologically free dynamical,system,Ideals,Maximal abelian subalgebra,Covering map}, language = {eng}, number = {3}, pages = {573583}, publisher = {Springer}, series = {Acta Applicandae Mathematicae}, title = {On the Exel Crossed Product of Topological Covering Maps}, url = {http://dx.doi.org/10.1007/s1044000893726}, volume = {108}, year = {2009}, }