Weakly-monotone C*-algebras as Exel-Laca algebras
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915103433031680 |
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| author | Crismale, Vitonofrio Del Vecchio, Simone Rossi, Stefano Wysoczański, Janusz |
| author_facet | Crismale, Vitonofrio Del Vecchio, Simone Rossi, Stefano Wysoczański, Janusz |
| contents | An abstract characterization of weakly monotone $C^*$-algebras, namely the concrete $C^*$-algebras generated by creators and annihilators acting on the so-called weakly monotone Fock spaces, is given in terms of (quotient of) suitable Exel-Laca algebras. The weakly monotone $C^*$-algebra indexed by $\mathbb{N}$ is shown to be a type-I $C^*$-algebra and its representation theory is entirely determined, whereas the weakly monotone $C^*$-algebra indexed by $\mathbb{Z}$ is shown not to be of type $I$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly-monotone C*-algebras as Exel-Laca algebras Crismale, Vitonofrio Del Vecchio, Simone Rossi, Stefano Wysoczański, Janusz Operator Algebras 46L05, 46L45, 46L35 An abstract characterization of weakly monotone $C^*$-algebras, namely the concrete $C^*$-algebras generated by creators and annihilators acting on the so-called weakly monotone Fock spaces, is given in terms of (quotient of) suitable Exel-Laca algebras. The weakly monotone $C^*$-algebra indexed by $\mathbb{N}$ is shown to be a type-I $C^*$-algebra and its representation theory is entirely determined, whereas the weakly monotone $C^*$-algebra indexed by $\mathbb{Z}$ is shown not to be of type $I$. |
| title | Weakly-monotone C*-algebras as Exel-Laca algebras |
| topic | Operator Algebras 46L05, 46L45, 46L35 |
| url | https://arxiv.org/abs/2402.08435 |