We show isomorphism in C*-algebras through trace-preserving homotopy equivalence, highlighting implications for rigidity.
We show that two simple, separable, nuclear, and Z₀ -stable C* -algebras are isomorphic if they are trace-preservingly homotopy equivalent. This result does not assume the Universal Coefficient Theorem and can be viewed as a tracial stably projectionless analogue of the homotopy rigidity theorem for Kirchberg algebras.
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Castillejos et al. (2026) studied this question.
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