A quantized version of the Sierpinski gasket is proposed, on purely topological grounds, as a C*-algebra A infinity with a suitable form of self-similarity. Several properties of A infinity are studied, in particular its nuclearity, the structure of ideals as well as the description of irreducible representations and extremal traces. A harmonic structure is introduced, giving rise to a self-similar Dirichlet form E. A spectral triple is also constructed, extending the one already known for the classical gasket, from which E can be reconstructed. Moreover we show that A infinity is a compact quantum metric space.

Cipriani, F., Guido, D., Isola, T., Sauvageot, J.-. (2022). A noncommutative Sierpinski gasket. JOURNAL OF FUNCTIONAL ANALYSIS, 283(5) [10.1016/j.jfa.2022.109563].

A noncommutative Sierpinski gasket

Guido D.
;
Isola T.;
2022-01-01

Abstract

A quantized version of the Sierpinski gasket is proposed, on purely topological grounds, as a C*-algebra A infinity with a suitable form of self-similarity. Several properties of A infinity are studied, in particular its nuclearity, the structure of ideals as well as the description of irreducible representations and extremal traces. A harmonic structure is introduced, giving rise to a self-similar Dirichlet form E. A spectral triple is also constructed, extending the one already known for the classical gasket, from which E can be reconstructed. Moreover we show that A infinity is a compact quantum metric space.
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Dirichlet forms
Self-similar fractals
Noncommutative geometry and spectral triples
Cipriani, F., Guido, D., Isola, T., Sauvageot, J.-. (2022). A noncommutative Sierpinski gasket. JOURNAL OF FUNCTIONAL ANALYSIS, 283(5) [10.1016/j.jfa.2022.109563].
Cipriani, Feg; Guido, D; Isola, T; Sauvageot, J-
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/302797
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