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Simple skew category algebras associated with minimal partially defined dynamical systems
University West, Department of Engineering Science, Division of Natural Sciences and Electrical and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
University of Copenhagen, Department of Mathematical Sciences.
2013 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 33, no 9, p. 4157-4171Article in journal (Refereed) Published
Abstract [en]

In this article, we continue our study of category dynamical systems, that is functors s from a category G to Topop, and their corresponding skew category algebras. Suppose that the spaces s(e), for e ∈ ob(G), are compact Hausdorff. We show that if (i) the skew category algebra is simple, then (ii) G is inverse connected, (iii) s is minimal and (iv) s is faithful. We also show that if G is a locally abelian groupoid, then (i) is equivalent to (ii), (iii) and (iv). Thereby, we generalize results by Öinert for skew group algebras to a large class of skew category algebras.

Place, publisher, year, edition, pages
2013. Vol. 33, no 9, p. 4157-4171
Keywords [en]
Category dynamical systems, Minimality, Partially defined dynamical systems, Simplicity, Skew category algebras
National Category
Mathematics
Research subject
ENGINEERING, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-5311DOI: 10.3934/dcds.2013.33.4157ISI: 000316725400015Scopus ID: 2-s2.0-84876017758ISBN: 10780947 (ISSN) OAI: oai:DiVA.org:hv-5311DiVA, id: diva2:617624
Available from: 2013-04-24 Created: 2013-04-24 Last updated: 2018-04-11Bibliographically approved

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