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Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics
Universidade Federal de Santa Catarina, BRA.
Universidade Federal de Santa Catarina, BRA.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.ORCID iD: 0000-0001-8095-0820
Universidade Federal de Santa Catarina, BRA.
2019 (English)In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 31, no 3, p. 543-562Article in journal (Refereed) Published
Abstract [en]

Given a partial action π of an inverse semigroup S on a ring A {\mathcal{A}}, one may construct its associated skew inverse semigroup ring A π S {\mathcal{A}\rtimes-{\pi}S}. Our main result asserts that, when A {\mathcal{A}} is commutative, the ring A π S {\mathcal{A}\rtimes-{\pi}S} is simple if, and only if, A {\mathcal{A}} is a maximal commutative subring of A π S {\mathcal{A}\rtimes-{\pi}S} and A {\mathcal{A}} is S-simple. We apply this result in the context of topological inverse semigroup actions to connect simplicity of the associated skew inverse semigroup ring with topological properties of the action. Furthermore, we use our result to present a new proof of the simplicity criterion for a Steinberg algebra A R (g) {A-{R}(\mathcal{G})} associated with a Hausdorff and ample groupoid g {\mathcal{G}}. © 2018 Walter de Gruyter GmbH, Berlin/Boston.

Place, publisher, year, edition, pages
De Gruyter , 2019. Vol. 31, no 3, p. 543-562
Keywords [en]
inverse semigroup, partial action, Skew inverse semigroup ring, Steinberg algebra
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:bth-17415DOI: 10.1515/forum-2018-0160ISI: 000465554800001Scopus ID: 2-s2.0-85057335724OAI: oai:DiVA.org:bth-17415DiVA, id: diva2:1270396
Available from: 2018-12-13 Created: 2018-12-13 Last updated: 2019-05-21Bibliographically approved

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Öinert, Johan

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CiteExportLink to record
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  • apa
  • harvard1
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  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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