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arXiv · 2601.02835

Quantum isometry groups of log-Laplacians on Cuntz--Krieger algebras

Amaury Freslon·Dimitris Michail Gerontogiannis·Adam Skalski
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Abstract

We compute the quantum isometry groups of Cuntz-Krieger algebras endowed with the spectral triples coming from the Ahlfors regular structure of the underlying topological Markov chain. This allows us to exhibit a new family of compact quantum groups, mixing features from quantum automorphism groups of graphs and easy quantum groups. Contrary to the classical isometry groups, whose actions on the Cuntz-Krieger algebras are never ergodic, the quantum isometry group acts ergodically in the case of the Cuntz algebra. This also leads to the construction of a (genuinely quantum) ergodic action of a compact matrix quantum group on the Cantor space.

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Amaury Freslon, Dimitris Michail Gerontogiannis, Adam Skalski. 2026-01-06. Quantum isometry groups of log-Laplacians on Cuntz--Krieger algebras. https://arxiv.org/abs/2601.02835

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