Advanced

Outer Partial Actions and Partial Skew Group Rings

Nystedt, Patrik and Öinert, Johan LU (2015) In Canadian Journal of Mathematics 67(5). p.1144-1160
Abstract
We extend the classical notion of an outer action alpha of a group G on a unital ring A to the case when alpha is a partial action on ideals, all of which have local units. We show that if alpha is an outer partial action of an abelian group G, then its associated partial skew group ring A(star alpha) G is simple if and only if A is G-simple. This result is applied to partial skew group rings associated with two different types of partial dynamical systems.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
outer action, partial action, minimality, topological dynamics, partial, skew group ring, simplicity
in
Canadian Journal of Mathematics
volume
67
issue
5
pages
1144 - 1160
publisher
Canadian Mathematical Society
external identifiers
  • wos:000362152600008
  • scopus:84976400598
ISSN
0008-414X
DOI
10.4153/CJM-2014-043-8
language
English
LU publication?
yes
id
5e71b36f-9981-4da2-8f91-c8704d9a6d1f (old id 8221337)
date added to LUP
2015-11-30 13:40:50
date last changed
2017-01-01 05:30:33
@article{5e71b36f-9981-4da2-8f91-c8704d9a6d1f,
  abstract     = {We extend the classical notion of an outer action alpha of a group G on a unital ring A to the case when alpha is a partial action on ideals, all of which have local units. We show that if alpha is an outer partial action of an abelian group G, then its associated partial skew group ring A(star alpha) G is simple if and only if A is G-simple. This result is applied to partial skew group rings associated with two different types of partial dynamical systems.},
  author       = {Nystedt, Patrik and Öinert, Johan},
  issn         = {0008-414X},
  keyword      = {outer action,partial action,minimality,topological dynamics,partial,skew group ring,simplicity},
  language     = {eng},
  number       = {5},
  pages        = {1144--1160},
  publisher    = {Canadian Mathematical Society},
  series       = {Canadian Journal of Mathematics},
  title        = {Outer Partial Actions and Partial Skew Group Rings},
  url          = {http://dx.doi.org/10.4153/CJM-2014-043-8},
  volume       = {67},
  year         = {2015},
}