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Simple skew category algebras associated with minimal partially defined dynamical systems

Nystedt, Patrik and Öinert, Johan LU (2013) In Discrete and Continuous Dynamical Systems. Series A 33(9). p.4157-4171
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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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
partially defined dynamical systems, Skew category algebras, category dynamical systems, minimality, simplicity
in
Discrete and Continuous Dynamical Systems. Series A
volume
33
issue
9
pages
4157 - 4171
publisher
American Institute of Mathematical Sciences
external identifiers
  • wos:000316725400015
  • scopus:84876017758
ISSN
1553-5231
DOI
10.3934/dcds.2013.33.4157
language
English
LU publication?
yes
id
0960ad5e-e5af-4de9-82b8-04b8c0b4e718 (old id 3616386)
date added to LUP
2016-04-01 09:52:14
date last changed
2022-02-17 04:21:17
@article{0960ad5e-e5af-4de9-82b8-04b8c0b4e718,
  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.}},
  author       = {{Nystedt, Patrik and Öinert, Johan}},
  issn         = {{1553-5231}},
  keywords     = {{partially defined dynamical systems; Skew category algebras; category dynamical systems; minimality; simplicity}},
  language     = {{eng}},
  number       = {{9}},
  pages        = {{4157--4171}},
  publisher    = {{American Institute of Mathematical Sciences}},
  series       = {{Discrete and Continuous Dynamical Systems. Series A}},
  title        = {{Simple skew category algebras associated with minimal partially defined dynamical systems}},
  url          = {{http://dx.doi.org/10.3934/dcds.2013.33.4157}},
  doi          = {{10.3934/dcds.2013.33.4157}},
  volume       = {{33}},
  year         = {{2013}},
}