$C^*$-algebras associated to directed graphs of groups, and models of Kirchberg algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911789294288896 |
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| author | Wu, Victor |
| author_facet | Wu, Victor |
| contents | We introduce $C^*$-algebras associated to directed graphs of groups. In particular, we associate a combinatorial $C^*$-algebra to each row-finite directed graph of groups with no sources, and show that this $C^*$-algebra is Morita equivalent to the crossed product coming from the corresponding group action on the boundary of a directed tree. Finally, we show that these $C^*$-algebras (and their Morita equivalent crossed products) contain the class of stable UCT Kirchberg algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^*$-algebras associated to directed graphs of groups, and models of Kirchberg algebras Wu, Victor Operator Algebras 46L05 (Primary), 46L35, 20E08 (Secondary) We introduce $C^*$-algebras associated to directed graphs of groups. In particular, we associate a combinatorial $C^*$-algebra to each row-finite directed graph of groups with no sources, and show that this $C^*$-algebra is Morita equivalent to the crossed product coming from the corresponding group action on the boundary of a directed tree. Finally, we show that these $C^*$-algebras (and their Morita equivalent crossed products) contain the class of stable UCT Kirchberg algebras. |
| title | $C^*$-algebras associated to directed graphs of groups, and models of Kirchberg algebras |
| topic | Operator Algebras 46L05 (Primary), 46L35, 20E08 (Secondary) |
| url | https://arxiv.org/abs/2403.02849 |