Simplicity of partial skew group rings with applications to Leavitt path algebras and topological dynamics
(2014) In Journal of Algebra 420. p.201-216- Abstract
- Let A be a commutative and associative ring (not necessarily unital), G a group and α a partial action of G on ideals of A, all of which have local units. We show that A is maximal commutative in the partial skew group ring A*G if and only if A has the ideal intersection property in A*G. From this we derive a criterion for simplicity of A*G in terms of maximal commutativity and G-simplicity of A. We also provide two applications of our main results. First, we give a new proof of the simplicity criterion for Leavitt path algebras, as well as a new proof of the Cuntz–Krieger uniqueness theorem. Secondly, we study topological dynamics arising from partial actions on clopen subsets of a compact set.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4631450
- author
- Gonçalves, Daniel ; Öinert, Johan LU and Royer, Danilo
- organization
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Partial skew group ring, Leavitt path algebra, Partial topological dynamics, Simplicity
- in
- Journal of Algebra
- volume
- 420
- pages
- 201 - 216
- publisher
- Elsevier
- external identifiers
-
- wos:000343020900011
- scopus:84908556969
- ISSN
- 0021-8693
- DOI
- 10.1016/j.jalgebra.2014.07.027
- language
- English
- LU publication?
- yes
- id
- 56a2aaac-d83a-4736-a1ad-efdafeeaf95f (old id 4631450)
- date added to LUP
- 2016-04-01 09:53:14
- date last changed
- 2022-01-25 17:36:03
@article{56a2aaac-d83a-4736-a1ad-efdafeeaf95f, abstract = {{Let A be a commutative and associative ring (not necessarily unital), G a group and α a partial action of G on ideals of A, all of which have local units. We show that A is maximal commutative in the partial skew group ring A*G if and only if A has the ideal intersection property in A*G. From this we derive a criterion for simplicity of A*G in terms of maximal commutativity and G-simplicity of A. We also provide two applications of our main results. First, we give a new proof of the simplicity criterion for Leavitt path algebras, as well as a new proof of the Cuntz–Krieger uniqueness theorem. Secondly, we study topological dynamics arising from partial actions on clopen subsets of a compact set.}}, author = {{Gonçalves, Daniel and Öinert, Johan and Royer, Danilo}}, issn = {{0021-8693}}, keywords = {{Partial skew group ring; Leavitt path algebra; Partial topological dynamics; Simplicity}}, language = {{eng}}, pages = {{201--216}}, publisher = {{Elsevier}}, series = {{Journal of Algebra}}, title = {{Simplicity of partial skew group rings with applications to Leavitt path algebras and topological dynamics}}, url = {{http://dx.doi.org/10.1016/j.jalgebra.2014.07.027}}, doi = {{10.1016/j.jalgebra.2014.07.027}}, volume = {{420}}, year = {{2014}}, }