Skew category algebras associated with partially defined dynamical systems
2012 (English)In: International Journal of Mathematics, ISSN 0129-167X, Vol. 23, no 4, 16- p.Article in journal (Refereed) Published
We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor s from a category G to Top^op and show that it defines what we call a skew category algebra AxG. We study the connection between topological freeness of s and, on the one hand, ideal properties of AxG and, on the other hand, maximal commutativity of A in AxG. In particular, we show that if G is a groupoid and for each e in ob(G) the group of all morphisms from e to e is countable and the topological space s(e) is Tychonoff and Baire, then the following assertions are equivalent: (i) s is topologically free; (ii) A has the ideal intersection property, that is if I is a nonzero ideal of AxG, then I \cap A is not equal to zero; (iii) the ring A is a maximal abelian complex subalgebra of AxG. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group of integers to a large class of groupoids.
Place, publisher, year, edition, pages
Singapore, 2012. Vol. 23, no 4, 16- p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:hv:diva-3582DOI: 10.1142/S0129167X12500401ISI: 000301503200009ScopusID: 2-s2.0-84860197662OAI: oai:DiVA.org:hv-3582DiVA: diva2:439445