Simple skew category algebras associated with minimal partially defined dynamical systems
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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.
Originalsprog | Engelsk |
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Tidsskrift | Discrete and Continuous Dynamical Systems. Series A |
Vol/bind | 33 |
Udgave nummer | 9 |
Sider (fra-til) | 4157-4171 |
ISSN | 1078-0947 |
DOI | |
Status | Udgivet - 2013 |
ID: 117199944