QUANTUM ISOMETRY GROUPS OF LOG-LAPLACIANS ON CUNTZ-KRIEGER ALGEBRAS

Speaker(s)

DIMITRIS M. GERONTOGIANNIS

Affiliation

IMPAN, Warszawa, Poland

Language of the talk

English

Date

March 11, 2026, 5:15 p.m.

Information about the event

IMPAN - Room 405 & zoom

Title in Polish

QUANTUM ISOMETRY GROUPS OF LOG-LAPLACIANS ON CUNTZ-KRIEGER ALGEBRAS

Seminar

North Atlantic Noncommutative Geometry Seminar

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In recent work with Magnus Goffeng and Bram Mesland, we showed that Cuntz-Krieger algebras admit canonical spectral triples via the log-Laplacian. This talk concerns the quantum symmetries preserving this differential structure. They lead to a new family of compact quantum groups where features of quantum automorphism groups of graphs and easy quantum groups are mixed. 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. Based on joint work with Amaury Freslon and Adam Skalski.

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