English

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 AHD\mathcal{HD} algebra, when K1K_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 CC^*-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}
}