Files in this item
Normalish amenable subgroups of the R. Thompson groups
Item metadata
dc.contributor.author | Bleak, Collin P. | |
dc.date.accessioned | 2022-09-08T23:45:19Z | |
dc.date.available | 2022-09-08T23:45:19Z | |
dc.date.issued | 2021-09-09 | |
dc.identifier | 274345252 | |
dc.identifier | 844eae7d-20ab-4e53-9f47-1a24456617c9 | |
dc.identifier | 85116583267 | |
dc.identifier | 000702147800009 | |
dc.identifier.citation | Bleak , C P 2021 , ' Normalish amenable subgroups of the R. Thompson groups ' , International Journal of Foundations of Computer Science , vol. 32 , no. 06 , pp. 785-800 . https://doi.org/10.1142/s0129054121420089 | en |
dc.identifier.issn | 0129-0541 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/100901235 | |
dc.identifier.uri | https://hdl.handle.net/10023/25979 | |
dc.description | Funding: UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/R032866/1. | en |
dc.description.abstract | Results 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.format.extent | 398416 | |
dc.language.iso | eng | |
dc.relation.ispartof | International Journal of Foundations of Computer Science | en |
dc.subject | Thompson's groups | en |
dc.subject | Amenable | en |
dc.subject | C*-simplicity | en |
dc.subject | Regular language | en |
dc.subject | Normalish | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Normalish amenable subgroups of the R. Thompson groups | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. School of Mathematics and Statistics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1142/s0129054121420089 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2022-09-09 | |
dc.identifier.grantnumber | EP/R032866/1 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.