Simple Skew Category Algebras Associated with Minimal Partially Defined Dynamical Systems

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.