Simple skew category algebras associated with minimal partially defined dynamical systems
Patrik Nystedt Johan Öinert
Discrete & Continuous Dynamical Systems - A 2013, 33(9): 4157-4171 doi: 10.3934/dcds.2013.33.4157
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.
keywords: simplicity. Skew category algebras partially defined dynamical systems category dynamical systems minimality

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