TY - JOUR

T1 - Simple skew category algebras associated with minimal partially defined dynamical systems

AU - Nystedt, Patrik

AU - Öinert, Per Johan

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

U2 - 10.3934/dcds.2013.33.4157

DO - 10.3934/dcds.2013.33.4157

M3 - Journal article

VL - 33

SP - 4157

EP - 4171

JO - Discrete and Continuous Dynamical Systems. Series A

JF - Discrete and Continuous Dynamical Systems. Series A

SN - 1078-0947

IS - 9

ER -