Subhomogeneity in the classification of real rank zero C*-algebras
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916467144916992 |
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| author | An, Qingnan Eilers, Søren Gong, Guihua Liu, Zhichao |
| author_facet | An, Qingnan Eilers, Søren Gong, Guihua Liu, Zhichao |
| contents | In this paper, we construct a class of ASH algebras of real rank zero and stable rank one which is not K-pure. Then we show the following:
(i) There exists a real rank zero inductive limit of 1-dimensional noncommutative CW complexes which is not an A$\mathcal{HD}$ algebra, when $K_1$ is torsion free or has bounded torsion.
(ii) Total K-theory is not a complete invariant for ASH algebras of real rank zero.
(iii) There are obstructions both in the total K-theory of ideals and quotients in the classification of $C^*$-algebras of real rank zero and stable rank one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02173 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subhomogeneity in the classification of real rank zero C*-algebras An, Qingnan Eilers, Søren Gong, Guihua Liu, Zhichao Operator Algebras In this paper, we construct a class of ASH algebras of real rank zero and stable rank one which is not K-pure. Then we show the following: (i) There exists a real rank zero inductive limit of 1-dimensional noncommutative CW complexes which is not an A$\mathcal{HD}$ algebra, when $K_1$ is torsion free or has bounded torsion. (ii) Total K-theory is not a complete invariant for ASH algebras of real rank zero. (iii) There are obstructions both in the total K-theory of ideals and quotients in the classification of $C^*$-algebras of real rank zero and stable rank one. |
| title | Subhomogeneity in the classification of real rank zero C*-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2411.02173 |