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On the Exel crossed product of topological covering maps
University of Southern Denmark.
Lund University. (Matematik/tillämpad matematik)ORCID iD: 0000-0003-4554-6528
2009 (English)In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, ISSN 0167-8019, Vol. 108, no 3, p. 573-583Article in journal (Refereed) Published
Abstract [en]

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)⋊ α,ℒℕintroduced 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)⋊ α,ℒℕis a maximal abelian C *-subalgebra of C(X)⋊ α,ℒN; any nontrivial two sided ideal of C(X)⋊ α,ℒℕhas non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊ α,ℒℕis faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product C *-algebras of homeomorphism dynamical systems. 

Place, publisher, year, edition, pages
Springer, 2009. Vol. 108, no 3, p. 573-583
Keywords [en]
Crossed product algebra, Topologically free dynamical, system, Ideals, Maximal abelian subalgebra, Covering map
National Category
Mathematical Analysis Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-22075DOI: 10.1007/s10440-008-9372-6ISI: 000271941500008Scopus ID: 2-s2.0-71449107536OAI: oai:DiVA.org:mdh-22075DiVA, id: diva2:682621
Funder
Swedish Research CouncilAvailable from: 2013-12-28 Created: 2013-10-23 Last updated: 2017-12-06Bibliographically approved

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Publisher's full textScopushttp://dx.doi.org/10.1007/s10440-008-9372-6

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Silvestrov, Sergei

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