Heat operators and isometry groups of Cuntz-Krieger algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912491298095104 |
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| author | Gerontogiannis, Dimitris Michail Goffeng, Magnus Mesland, Bram |
| author_facet | Gerontogiannis, Dimitris Michail Goffeng, Magnus Mesland, Bram |
| contents | This paper introduces heat semigroups of topological Markov chains and Cuntz-Krieger algebras by means of spectral noncommutative geometry. Using recent advances on the logarithmic Dirichlet Laplacian on Ahlfors regular metric-measure spaces, we construct spectral triples on Cuntz-Krieger algebras from singular integral operators. These spectral triples exhaust odd K-homology and for Cuntz algebras we can compute their heat operators explicitly as Riesz potential operators. We also describe their isometry group in terms of the automorphism group of the underlying directed graph and prove that the Voiculescu noncommutative topological entropy vanishes on isometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heat operators and isometry groups of Cuntz-Krieger algebras Gerontogiannis, Dimitris Michail Goffeng, Magnus Mesland, Bram Operator Algebras Dynamical Systems Functional Analysis Quantum Algebra Spectral Theory 37B10, 46L80, 47A10, 58B34 This paper introduces heat semigroups of topological Markov chains and Cuntz-Krieger algebras by means of spectral noncommutative geometry. Using recent advances on the logarithmic Dirichlet Laplacian on Ahlfors regular metric-measure spaces, we construct spectral triples on Cuntz-Krieger algebras from singular integral operators. These spectral triples exhaust odd K-homology and for Cuntz algebras we can compute their heat operators explicitly as Riesz potential operators. We also describe their isometry group in terms of the automorphism group of the underlying directed graph and prove that the Voiculescu noncommutative topological entropy vanishes on isometries. |
| title | Heat operators and isometry groups of Cuntz-Krieger algebras |
| topic | Operator Algebras Dynamical Systems Functional Analysis Quantum Algebra Spectral Theory 37B10, 46L80, 47A10, 58B34 |
| url | https://arxiv.org/abs/2406.07416 |