Finitely generated weakly monotone C*-algebra
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929681180131328 |
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| author | Griseta, Maria Elena Wysoczański, Janusz |
| author_facet | Griseta, Maria Elena Wysoczański, Janusz |
| contents | We consider the $C^*$-algebra generated by finitely many annihilation operators acting on the weakly monotone Fock space, and we call it weakly monotone $C^*$-algebra. We give an abstract representation for this algebra, showing that it is isomorphic to a suitable quotient of a Cuntz-Krieger $C^*$-algebra $\mathcal{O}_A$ corresponding to a suitable matrix $A$. Furthermore, we show that the diagonal subalgebra of the weakly monotone $C^*$-algebra is a MASA and we give the detailed description of its Gelfand spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finitely generated weakly monotone C*-algebra Griseta, Maria Elena Wysoczański, Janusz Operator Algebras 46L05, 46K10 We consider the $C^*$-algebra generated by finitely many annihilation operators acting on the weakly monotone Fock space, and we call it weakly monotone $C^*$-algebra. We give an abstract representation for this algebra, showing that it is isomorphic to a suitable quotient of a Cuntz-Krieger $C^*$-algebra $\mathcal{O}_A$ corresponding to a suitable matrix $A$. Furthermore, we show that the diagonal subalgebra of the weakly monotone $C^*$-algebra is a MASA and we give the detailed description of its Gelfand spectrum. |
| title | Finitely generated weakly monotone C*-algebra |
| topic | Operator Algebras 46L05, 46K10 |
| url | https://arxiv.org/abs/2402.19081 |