Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908761801621504 |
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| author | Austad, Are Raum, Sven |
| author_facet | Austad, Are Raum, Sven |
| contents | We introduce the $\ell^1$-ideal intersection property for crossed product C*-algebras. It is implied by C*-simplicity as well as C*-uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups, arbitrary linear groups over the integers in a number field and arbitrary virtually polycyclic groups have the $\ell^1$-ideal intersection property. On the way, we extend previous results on C*-uniqueness of $\mathrm{L}^1$-groupoid algebras to the general twisted setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01027 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems Austad, Are Raum, Sven Operator Algebras Dynamical Systems Group Theory We introduce the $\ell^1$-ideal intersection property for crossed product C*-algebras. It is implied by C*-simplicity as well as C*-uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups, arbitrary linear groups over the integers in a number field and arbitrary virtually polycyclic groups have the $\ell^1$-ideal intersection property. On the way, we extend previous results on C*-uniqueness of $\mathrm{L}^1$-groupoid algebras to the general twisted setting. |
| title | Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems |
| topic | Operator Algebras Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2301.01027 |