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Miyashita Action in Strongly Groupoid Graded Rings

Öinert, Johan LU and Lundström, Patrik (2012) In International Electronic Journal of Algebra 11. p.46-63
Abstract
We determine the commutant of homogeneous subrings in strongly

groupoid graded rings in terms of an action on the ring induced by the grading. Thereby we generalize a classical result of Miyashita from the group graded case to the groupoid graded situation. In the end of the article we exemplify this result. To this end, we show, by an explicit construction, that given a finite groupoid G, equipped with a nonidentity morphism t : d(t) \to c(t), there is a strongly G-graded ring R with the properties that each R_s, for s \in G, is nonzero and R_t is a nonfree left R_{c(t)}-module.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
graded rings, commutants, groupoid actions, matrix algebras
in
International Electronic Journal of Algebra
volume
11
pages
46 - 63
publisher
Istanbul : Abdullah Hamanci
ISSN
1306-6048
language
English
LU publication?
no
id
ab00e0c1-82cb-4d80-a46f-47e133167977 (old id 3409302)
alternative location
http://www.ieja.net/files/papers/volume-11/Volume-10--2011/5-V11-2012.pdf
date added to LUP
2013-03-22 21:02:57
date last changed
2016-04-16 00:40:02
@article{ab00e0c1-82cb-4d80-a46f-47e133167977,
  abstract     = {We determine the commutant of homogeneous subrings in strongly<br/><br>
groupoid graded rings in terms of an action on the ring induced by the grading. Thereby we generalize a classical result of Miyashita from the group graded case to the groupoid graded situation. In the end of the article we exemplify this result. To this end, we show, by an explicit construction, that given a finite groupoid G, equipped with a nonidentity morphism t : d(t) \to c(t), there is a strongly G-graded ring R with the properties that each R_s, for s \in G, is nonzero and R_t is a nonfree left R_{c(t)}-module.},
  author       = {Öinert, Johan and Lundström, Patrik},
  issn         = {1306-6048},
  keyword      = {graded rings,commutants,groupoid actions,matrix algebras},
  language     = {eng},
  pages        = {46--63},
  publisher    = {Istanbul : Abdullah Hamanci},
  series       = {International Electronic Journal of Algebra},
  title        = {Miyashita Action in Strongly Groupoid Graded Rings},
  volume       = {11},
  year         = {2012},
}