Subhomogeneity in the classification of real rank zero C*-algebras
Operator Algebras
2024-11-05 v1
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 algebra, when 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 -algebras of real rank zero and stable rank one.
Keywords
Cite
@article{arxiv.2411.02173,
title = {Subhomogeneity in the classification of real rank zero C*-algebras},
author = {Qingnan An and Søren Eilers and Guihua Gong and Zhichao Liu},
journal= {arXiv preprint arXiv:2411.02173},
year = {2024}
}