Skew category algebras associated with partially defined dynamical systems

Summary, in English

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 Topop and show that it defines what we call a skew category algebra A ⋊ G. We study the connection between topological freeness of s and, on the one hand, ideal properties of A ⋊ G and, on the other hand, maximal commutativity of A in A ⋊ G. In particular, we show that if G is a groupoid and for each e ∈ ob(G) the group of all morphisms e → 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, i.e. if I is a nonzero ideal of A ⋊ G, then I ∩ A ≠ {0}; (iii) the ring A is a maximal abelian complex subalgebra of A ⋊ G. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group of integers to a large class of groupoids.

• Författare: Patrik Lundström; Johan Öinert
• Publiceringsår: 2012
• Språk: Engelska
• Sidor: 1-1250040
• Publikation/Tidskrift/Serie: International Journal of Mathematics
• Volym: 23
• Issue: 4
• Länkar: http://arxiv.org/abs/1006.4776; http://dx.doi.org/10.1142/S0129167X12500401
• Dokumenttyp: Artikel i tidskrift
• Förlag: World Scientific Publishing
• Ämne: Mathematics
• Nyckelord: partially defined dynamical systems; category dynamical systems; Skew category algebras; topological freeness; maximal commutative subrings; ideals
• Status: Published
• Forskningsgrupp: Non-commutative Geometry
• ISBN/ISSN/Övrigt: ISSN: 0129-167X