arXiv subjects

Baukje Debets

Publications and source records attributed to Baukje Debets.

2 recordsLinked to original sources

arXiv2025

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

We show that two simple, separable, nuclear and $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-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.

math.OA↗

arXiv2019

Pure infiniteness and paradoxicality for graph $C^*$-algebras

We obtain necessary and sufficient conditions for pure infiniteness of the path groupoid $C^*$-algebra of a row-finite graph without sinks. In particular we show that for such a path groupoid $\mathcal{G}_E$, the properties of being essential principal and the existence of a basis of $(\mathcal{G}_E^a, 2, 1)$-paradoxical sets for the topology are not only sufficient, but also necessary.

math.OA↗