1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Department of Engineering Science, University West, Sweden3 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
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.
Discrete and Continuous Dynamical Systems. Series a, 2013, Vol 33, Issue 9, p. 4157-4171