Wold Decomposition and C*-envelopes of Self-Similar Semigroup Actions on Graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913346276556800 |
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| author | Li, Boyu Yang, Dilian |
| author_facet | Li, Boyu Yang, Dilian |
| contents | We study the Wold decomposition for representations of a self-similar semigroup $P$ action on a directed graph $E$. We then apply this decomposition to the case where $P=\mathbb{N}$ to study the C*-envelope of the associated universal non-selfadjoint operator algebra $\mathcal{A}_{\mathbb{N}, E}$ by carefully constructing explicit non-trivial dilations for non-boundary representations. In particular, it is shown that the C*-envelope of $\mathcal{A}_{\mathbb{N}, E}$ coincides with the self-similar C*-algebra $\mathcal{O}_{\mathbb{Z}, E}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10108 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Wold Decomposition and C*-envelopes of Self-Similar Semigroup Actions on Graphs Li, Boyu Yang, Dilian Operator Algebras Functional Analysis We study the Wold decomposition for representations of a self-similar semigroup $P$ action on a directed graph $E$. We then apply this decomposition to the case where $P=\mathbb{N}$ to study the C*-envelope of the associated universal non-selfadjoint operator algebra $\mathcal{A}_{\mathbb{N}, E}$ by carefully constructing explicit non-trivial dilations for non-boundary representations. In particular, it is shown that the C*-envelope of $\mathcal{A}_{\mathbb{N}, E}$ coincides with the self-similar C*-algebra $\mathcal{O}_{\mathbb{Z}, E}$. |
| title | Wold Decomposition and C*-envelopes of Self-Similar Semigroup Actions on Graphs |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2307.10108 |