An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909398255796224 |
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| author | Larki, Hossein |
| author_facet | Larki, Hossein |
| contents | We generalize the Li-Yang notion of self-similar $k$-graph $(G,Λ)$ and its $C^*$-algebra $\mathcal{O}_{G,Λ}$ to any finitely aligned $k$-graph $Λ$. We then introduce an inverse semigroup model for $\mathcal{O}_{G,Λ}$ and analyze its tight groupoid and $C^*$-algebra via inverse semigroup methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity Larki, Hossein Operator Algebras 46L05 We generalize the Li-Yang notion of self-similar $k$-graph $(G,Λ)$ and its $C^*$-algebra $\mathcal{O}_{G,Λ}$ to any finitely aligned $k$-graph $Λ$. We then introduce an inverse semigroup model for $\mathcal{O}_{G,Λ}$ and analyze its tight groupoid and $C^*$-algebra via inverse semigroup methods. |
| title | An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity |
| topic | Operator Algebras 46L05 |
| url | https://arxiv.org/abs/2411.14027 |