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dc.contributor.authorBleak, Collin P.
dc.date.accessioned2022-09-08T23:45:19Z
dc.date.available2022-09-08T23:45:19Z
dc.date.issued2021-09-09
dc.identifier.citationBleak , C P 2021 , ' Normalish amenable subgroups of the R. Thompson groups ' , International Journal of Foundations of Computer Science , vol. Online Ready . https://doi.org/10.1142/s0129054121420089en
dc.identifier.issn0129-0541
dc.identifier.otherPURE: 274345252
dc.identifier.otherPURE UUID: 844eae7d-20ab-4e53-9f47-1a24456617c9
dc.identifier.otherORCID: /0000-0001-5790-1940/work/100901235
dc.identifier.otherScopus: 85116583267
dc.identifier.otherWOS: 000702147800009
dc.identifier.urihttp://hdl.handle.net/10023/25979
dc.descriptionFunding: UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/R032866/1.en
dc.description.abstractResults in C∗ algebras, of Matte Bon and Le Boudec, and of Haagerup and Olesen, apply to the R. Thompson groups F≤T≤V. These results together show that F is non-amenable if and only if T has a simple reduced C∗-algebra. In further investigations into the structure of C∗-algebras, Breuillard, Kalantar, Kennedy, and Ozawa introduce the notion of a normalish subgroup of a group G. They show that if a group G admits no non-trivial finite normal subgroups and no normalish amenable subgroups then it has a simple reduced C∗-algebra. Our chief result concerns the R. Thompson groups F<T<V; we show that there is an elementary amenable group E<F [where here, E≅…)≀Z)≀Z)≀Z] with E normalish in V. The proof given uses a natural partial action of the group V on a regular language determined by a synchronising automaton in order to verify a certain stability condition: once again highlighting the existence of interesting intersections of the theory of V with various forms of formal language theory.
dc.language.isoeng
dc.relation.ispartofInternational Journal of Foundations of Computer Scienceen
dc.rightsCopyright © 2021 World Scientific Publishing Co Pte Ltd. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1142/S0129054121420089.en
dc.subjectThompson's groupsen
dc.subjectAmenableen
dc.subjectC*-simplicityen
dc.subjectRegular languageen
dc.subjectNormalishen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleNormalish amenable subgroups of the R. Thompson groupsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1142/s0129054121420089
dc.description.statusPeer revieweden
dc.date.embargoedUntil2022-09-09
dc.identifier.grantnumberEP/R032866/1en


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