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Heat Operators and Isometry Groups of Cuntz–Krieger Algebras

Gerontogiannis, Dimitris M. ; Goffeng, Magnus LU orcid and Mesland, Bram (2025) In International Mathematics Research Notices 2025(6).
Abstract

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.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Mathematics Research Notices
volume
2025
issue
6
article number
rnaf054
publisher
Oxford University Press
external identifiers
  • scopus:105001189124
ISSN
1073-7928
DOI
10.1093/imrn/rnaf054
language
English
LU publication?
yes
id
270dce63-ddc5-4f77-8b26-3985f7b1fa5e
date added to LUP
2025-08-26 12:00:20
date last changed
2025-08-26 12:00:57
@article{270dce63-ddc5-4f77-8b26-3985f7b1fa5e,
  abstract     = {{<p>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.</p>}},
  author       = {{Gerontogiannis, Dimitris M. and Goffeng, Magnus and Mesland, Bram}},
  issn         = {{1073-7928}},
  language     = {{eng}},
  number       = {{6}},
  publisher    = {{Oxford University Press}},
  series       = {{International Mathematics Research Notices}},
  title        = {{Heat Operators and Isometry Groups of Cuntz–Krieger Algebras}},
  url          = {{http://dx.doi.org/10.1093/imrn/rnaf054}},
  doi          = {{10.1093/imrn/rnaf054}},
  volume       = {{2025}},
  year         = {{2025}},
}