Simple skew category algebras associated with minimal partially defined dynamical systems
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3616386
- author
- Nystedt, Patrik and Öinert, Johan LU
- organization
- publishing date
- 2013
- 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}}, }