Extension groups for the $C^*$-algebras associated with $λ$-graph systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911889551785984 |
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| author | Matsumoto, Kengo |
| author_facet | Matsumoto, Kengo |
| contents | A $λ$-graph system is a labeled Bratteli diagram with certain additional structure, which presents a subshift. The class of the $C^*$-algebras $\mathcal{O}_{\frak L}$ associated with the $λ$-graph systems is a generalized class of the class of Cuntz--Krieger algebras. In this paper, we will compute the strong extension groups $\operatorname{Ext}_{\operatorname{s}}(\mathcal{O}_{\frak L})$ for the $C^*$-algebras associated with $λ$-graph systems ${\frak L}$ and study their relation with the weak extension group $\operatorname{Ext}_{\operatorname{w}}(\mathcal{O}_{\frak L})$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_03204 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extension groups for the $C^*$-algebras associated with $λ$-graph systems Matsumoto, Kengo Operator Algebras K-Theory and Homology Primary 46L80, Secondary 19K33 A $λ$-graph system is a labeled Bratteli diagram with certain additional structure, which presents a subshift. The class of the $C^*$-algebras $\mathcal{O}_{\frak L}$ associated with the $λ$-graph systems is a generalized class of the class of Cuntz--Krieger algebras. In this paper, we will compute the strong extension groups $\operatorname{Ext}_{\operatorname{s}}(\mathcal{O}_{\frak L})$ for the $C^*$-algebras associated with $λ$-graph systems ${\frak L}$ and study their relation with the weak extension group $\operatorname{Ext}_{\operatorname{w}}(\mathcal{O}_{\frak L})$. |
| title | Extension groups for the $C^*$-algebras associated with $λ$-graph systems |
| topic | Operator Algebras K-Theory and Homology Primary 46L80, Secondary 19K33 |
| url | https://arxiv.org/abs/2405.03204 |