Simple skew category algebras associated with minimal partially defined dynamical systems

Patrik Nystedt; Johan Öinert

doi:10.3934/dcds.2013.33.4157

Article Contents

2013, Volume 33, Issue 9: 4157-4171. Doi: 10.3934/dcds.2013.33.4157

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Simple skew category algebras associated with minimal partially defined dynamical systems

Patrik Nystedt^1, and
Johan Öinert^2,

1.
University West, Department of Engineering Science, SE-46186 Trollhättan
2.
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø

Received: May 31, 2012

Revised: January 31, 2013

Published: August 2013

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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.

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Mathematics Subject Classification: Primary: 16W50, 16S99; Secondary: 54H20.

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