Subhomogeneity in the classification of real rank zero C*-algebras

Fuente: arXiv
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Autores principales: An, Qingnan, Eilers, Søren, Gong, Guihua, Liu, Zhichao
Formato: Preprint
Publicado: 2024
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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