Simple skew category algebras associated with minimal partially defined dynamical systems

Patrik Nystedt, Johan Öinert

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)

Abstract

In this article, we continue our study of category dynamical systems, that is functors s from a category G to Top^{op}, 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.
Original languageEnglish
Pages (from-to)4157-4171
JournalDiscrete and Continuous Dynamical Systems. Series A
Volume33
Issue number9
DOIs
Publication statusPublished - 2013

Subject classification (UKÄ)

  • Mathematics

Keywords

  • partially defined dynamical systems
  • Skew category algebras
  • category dynamical systems
  • minimality
  • simplicity

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