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On normalish subgroups of the R. Thompson groups
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dc.contributor.author | Bleak, Collin Patrick | |
dc.contributor.editor | Jonoska, Nataša | |
dc.contributor.editor | Savchuk, Dmytro | |
dc.date.accessioned | 2020-06-01T10:30:05Z | |
dc.date.available | 2020-06-01T10:30:05Z | |
dc.date.issued | 2020-05 | |
dc.identifier | 268029453 | |
dc.identifier | 19aef1e5-1239-4a18-b54b-e20940016d6f | |
dc.identifier | 85086183051 | |
dc.identifier | 85086183051 | |
dc.identifier | 000905606300003 | |
dc.identifier.citation | Bleak , C P 2020 , On normalish subgroups of the R. Thompson groups . in N Jonoska & D Savchuk (eds) , Developments in Language Theory : 24th International Conference, DLT 2020, Tampa, FL, USA, May 11–15, 2020, Proceedings . Lecture Notes in Computer Science , vol. 12086 , Springer , pp. 29-42 , 24th International Conference on Developments in Language Theory (DLT) , Tampa , Florida , United States , 11/05/20 . https://doi.org/10.1007/978-3-030-48516-0_3 | en |
dc.identifier.citation | conference | en |
dc.identifier.isbn | 9783030485153 | |
dc.identifier.isbn | 9783030485160 | |
dc.identifier.issn | 0302-9743 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/75248614 | |
dc.identifier.uri | https://hdl.handle.net/10023/20020 | |
dc.description | Funding: UK 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 synchronizing 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 | 14 | |
dc.format.extent | 169327 | |
dc.language.iso | eng | |
dc.publisher | Springer | |
dc.relation.ispartof | Developments in Language Theory | en |
dc.relation.ispartofseries | Lecture Notes in Computer Science | en |
dc.subject | Thompson's group | en |
dc.subject | Amenable | en |
dc.subject | C*-simplicity | en |
dc.subject | Regular language | en |
dc.subject | Synchronizing automata | en |
dc.subject | Group actions | en |
dc.subject | Normalish sub-groups | en |
dc.subject | Wreath product | en |
dc.subject | QA75 Electronic computers. Computer science | en |
dc.subject | Theoretical Computer Science | en |
dc.subject | Computer Science(all) | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA75 | en |
dc.title | On normalish subgroups of the R. Thompson groups | en |
dc.type | Conference item | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1007/978-3-030-48516-0_3 | |
dc.identifier.url | https://doi.org/10.1007/978-3-030-48516-0 | en |
dc.identifier.grantnumber | EP/R032866/1 | en |
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