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Simplicity of Skew Group Rings of Abelian Groups

Öinert, Johan LU (2014) In Communications in Algebra 42(2). p.831-841
Abstract
Necessary and sufficient conditions for simplicity of a general skew group ring A?(sigma)G are not known. In this article, we show that a skew group ring A?(sigma)G, of an abelian group G, is simple if and only if its centre is a field and A is G-simple. As an application, we show that a transformation group (X, G), where X is a compact Hausdorff space acted upon by an abelian group G, is minimal and faithful if and only if its associated skew group algebra C(X)?(sigma)G is simple.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Ideals, Minimality, Skew group rings, Simplicity, Transformation groups
in
Communications in Algebra
volume
42
issue
2
pages
831 - 841
publisher
Taylor & Francis
external identifiers
  • wos:000325788400024
  • scopus:84886435421
ISSN
0092-7872
DOI
10.1080/00927872.2012.727052
language
English
LU publication?
yes
id
7403b067-cb1b-44e3-86eb-c116493ba1f4 (old id 4157852)
date added to LUP
2013-12-05 09:20:42
date last changed
2017-10-22 03:15:15
@article{7403b067-cb1b-44e3-86eb-c116493ba1f4,
  abstract     = {Necessary and sufficient conditions for simplicity of a general skew group ring A?(sigma)G are not known. In this article, we show that a skew group ring A?(sigma)G, of an abelian group G, is simple if and only if its centre is a field and A is G-simple. As an application, we show that a transformation group (X, G), where X is a compact Hausdorff space acted upon by an abelian group G, is minimal and faithful if and only if its associated skew group algebra C(X)?(sigma)G is simple.},
  author       = {Öinert, Johan},
  issn         = {0092-7872},
  keyword      = {Ideals,Minimality,Skew group rings,Simplicity,Transformation groups},
  language     = {eng},
  number       = {2},
  pages        = {831--841},
  publisher    = {Taylor & Francis},
  series       = {Communications in Algebra},
  title        = {Simplicity of Skew Group Rings of Abelian Groups},
  url          = {http://dx.doi.org/10.1080/00927872.2012.727052},
  volume       = {42},
  year         = {2014},
}