Cartan subalgebras of C*-algebras associated with complex dynamical systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910771596754944 |
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| author | Ito, Kei |
| author_facet | Ito, Kei |
| contents | Let $R$ be a rational function with degree $\geq 2$ and $X$ be its Julia set, its Fatou set, or the Riemann sphere. Suppose that $X$ is not empty. We can regard $R$ as a continuous map from $X$ onto itself. Kajiwara and Watatani showed that in the case that $X$ is the Julia set, $C_0(X)$ is a maximal abelian subalgebra of $\mathcal{O}_R(X)$, where $\mathcal{O}_R(X)$ denotes the C*-algebra associated with the dynamical system $(X,R)$ introduced by them. In this paper, we develop their result and give the equivalent condition for $C_0(X)$ to be a Cartan subalgebra of $\mathcal{O}_R(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14860 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cartan subalgebras of C*-algebras associated with complex dynamical systems Ito, Kei Operator Algebras Dynamical Systems 46L55 Let $R$ be a rational function with degree $\geq 2$ and $X$ be its Julia set, its Fatou set, or the Riemann sphere. Suppose that $X$ is not empty. We can regard $R$ as a continuous map from $X$ onto itself. Kajiwara and Watatani showed that in the case that $X$ is the Julia set, $C_0(X)$ is a maximal abelian subalgebra of $\mathcal{O}_R(X)$, where $\mathcal{O}_R(X)$ denotes the C*-algebra associated with the dynamical system $(X,R)$ introduced by them. In this paper, we develop their result and give the equivalent condition for $C_0(X)$ to be a Cartan subalgebra of $\mathcal{O}_R(X)$. |
| title | Cartan subalgebras of C*-algebras associated with complex dynamical systems |
| topic | Operator Algebras Dynamical Systems 46L55 |
| url | https://arxiv.org/abs/2303.14860 |