Selfless reduced free products and graph products of $\mathrm{C}^\ast$-algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911258945519616 |
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| author | Flores, Felipe Klisse, Mario Cobhthaigh, Mícheál Ó Pagliero, Matteo |
| author_facet | Flores, Felipe Klisse, Mario Cobhthaigh, Mícheál Ó Pagliero, Matteo |
| contents | Under mild assumptions, we show that reduced free products and reduced graph products of $\mathrm{C}^\ast$-algebras are selfless in the sense of L. Robert, without assuming the rapid decay property. In particular, our main theorems yield numerous new examples of simple, monotracial $\mathrm{C}^\ast$-algebras with strict comparison, stable rank one, and admitting a unique unital embedding of the Jiang-Su algebra $\mathcal{Z}$ up to approximate unitary equivalence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_24675 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Selfless reduced free products and graph products of $\mathrm{C}^\ast$-algebras Flores, Felipe Klisse, Mario Cobhthaigh, Mícheál Ó Pagliero, Matteo Operator Algebras Functional Analysis 20E06, 20F55, 46L05, 46L09, 46M07 Under mild assumptions, we show that reduced free products and reduced graph products of $\mathrm{C}^\ast$-algebras are selfless in the sense of L. Robert, without assuming the rapid decay property. In particular, our main theorems yield numerous new examples of simple, monotracial $\mathrm{C}^\ast$-algebras with strict comparison, stable rank one, and admitting a unique unital embedding of the Jiang-Su algebra $\mathcal{Z}$ up to approximate unitary equivalence. |
| title | Selfless reduced free products and graph products of $\mathrm{C}^\ast$-algebras |
| topic | Operator Algebras Functional Analysis 20E06, 20F55, 46L05, 46L09, 46M07 |
| url | https://arxiv.org/abs/2510.24675 |