Atomic representations of R. Thompson's groups and Cuntz's algebra
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911905208074240 |
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| author | Brothier, Arnaud Wijesena, Dilshan |
| author_facet | Brothier, Arnaud Wijesena, Dilshan |
| contents | We continue to study Pythagorean unitary representation of Richard Thompson's groups $F,T,V$ and their extension to the Cuntz(-Dixmier) algebra. Any linear isometry from a Hilbert space to its direct sum square produces such. We focus on those arising from a finite-dimensional Hilbert space. We show that they decompose as a direct sum of a so-called diffuse part and an atomic part. We previously proved that the diffuse part is Ind-mixing: it does not contain induced representations of finite-dimensional ones. In this article, we fully describe the atomic part: it is a finite direct sum of irreducible monomial representations arising from a precise family of parabolic subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Atomic representations of R. Thompson's groups and Cuntz's algebra Brothier, Arnaud Wijesena, Dilshan Group Theory Operator Algebras We continue to study Pythagorean unitary representation of Richard Thompson's groups $F,T,V$ and their extension to the Cuntz(-Dixmier) algebra. Any linear isometry from a Hilbert space to its direct sum square produces such. We focus on those arising from a finite-dimensional Hilbert space. We show that they decompose as a direct sum of a so-called diffuse part and an atomic part. We previously proved that the diffuse part is Ind-mixing: it does not contain induced representations of finite-dimensional ones. In this article, we fully describe the atomic part: it is a finite direct sum of irreducible monomial representations arising from a precise family of parabolic subgroups. |
| title | Atomic representations of R. Thompson's groups and Cuntz's algebra |
| topic | Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2406.02967 |