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arXiv · 2411.02173

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

Qingnan An·Søren Eilers·Guihua Gong·Zhichao Liu
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Abstract

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.

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Qingnan An, Søren Eilers, Guihua Gong, Zhichao Liu. 2024-11-04. Subhomogeneity in the classification of real rank zero C*-algebras. https://arxiv.org/abs/2411.02173

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