English

A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras

Operator Algebras 2025-05-12 v2

Abstract

We show that two simple, separable, nuclear and Z0\mathcal{Z}_0-stable C\mathrm{C}^\ast-algebras are isomorphic if they are trace-preservingly homotopy equivalent. This result does not assume the UCT and can be viewed as a tracial stably projectionless analog of the homotopy rigidity theorem for Kirchberg algebras.

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Cite

@article{arxiv.2505.04857,
  title  = {A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras},
  author = {Jorge Castillejos and Baukje Debets and Gabor Szabo},
  journal= {arXiv preprint arXiv:2505.04857},
  year   = {2025}
}

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13 pages