2012/05/07 by Patrik Lundström, Lundström, Patrik, Johan Öinert +1
Mathematics · #16S99 #16W50 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #Rings and Algebras (math.RA) #math.DS #math.RA #msc:16S99 #msc:16W50 #msc:54H20
paper · pdf · doi:10.48550/arxiv.1205.1539
17 pages. arXiv admin note: substantial text overlap with arXiv:1006.4776
arxiv created 2012/05/07 · arxiv updated 2013/02/11
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.