Cartan subalgebras of C*-algebras associated with iterated function systems
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910776867946496 |
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| author | Ito, Kei |
| author_facet | Ito, Kei |
| contents | Let $X$ be a compact Hausdorff space, and let $γ$ be an iterated function system on $X$. Kajiwara and Watatani showed that if $γ$ is self-similar and satisfies the open set condition and some additional technical conditions, $C(X)$ is a maximal abelian subalgebra of the Kajiwara--Watatani algebra $Ø_γ$ associated with $γ$. In this paper, we extend their results by providing sufficient conditions under which $C(X)$ becomes a Cartan subalgebra of $Ø_γ$. Additionally, we present sufficient conditions under which $C(X)$ fails to be a masa of $Ø_γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cartan subalgebras of C*-algebras associated with iterated function systems Ito, Kei Operator Algebras 46L55 Let $X$ be a compact Hausdorff space, and let $γ$ be an iterated function system on $X$. Kajiwara and Watatani showed that if $γ$ is self-similar and satisfies the open set condition and some additional technical conditions, $C(X)$ is a maximal abelian subalgebra of the Kajiwara--Watatani algebra $Ø_γ$ associated with $γ$. In this paper, we extend their results by providing sufficient conditions under which $C(X)$ becomes a Cartan subalgebra of $Ø_γ$. Additionally, we present sufficient conditions under which $C(X)$ fails to be a masa of $Ø_γ$. |
| title | Cartan subalgebras of C*-algebras associated with iterated function systems |
| topic | Operator Algebras 46L55 |
| url | https://arxiv.org/abs/2501.04127 |