Quantum isometry groups of log-Laplacians on Cuntz--Krieger algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911520669040640 |
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| author | Freslon, Amaury Gerontogiannis, Dimitris Michail Skalski, Adam |
| author_facet | Freslon, Amaury Gerontogiannis, Dimitris Michail Skalski, Adam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02835 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum isometry groups of log-Laplacians on Cuntz--Krieger algebras Freslon, Amaury Gerontogiannis, Dimitris Michail Skalski, Adam Operator Algebras Quantum Algebra 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. |
| title | Quantum isometry groups of log-Laplacians on Cuntz--Krieger algebras |
| topic | Operator Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2601.02835 |