Comptes Rendus
no. 11
Geometry/Mathematical Physics
The spectral geometry of the equatorial Podleś sphere
[La géométrie spectrale de la sphère « équatoriale » de Podleś]

Présenté par : Alain Connes

Ludwik Da̧browski1 ; Giovanni Landi2 ; Mario Paschke3 ; Andrzej Sitarz4
1 Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014, Trieste, Italy
2 Dipartimento di Matematica e Informatica, Università di Trieste via A. Valerio 12/1, 34127, Trieste, Italy
3 Max-Planck-Institut für Mathematik in den Naturwissenschaften, 04103 Leipzig, Germany
4 Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 819-822.

Nous présentons une version légèrement modifiée des axiomes de la géométrie spectrale (réelle) au sens de Connes, qui permettent aux relations algébriques d'être satisfaites modulo les opérateurs compacts. Nous montrons que la sphère quantique « équatoriale » de Podleś est une géométrie spectrale et nous déterminons l'opérateur de Dirac et la structure réelle correspondante.

We propose a slight modification of the properties of a spectral geometry à la Connes, which allows for some of the algebraic relations to be satisfied only modulo compact operators. On the equatorial Podleś sphere we construct Uq(su(2))-equivariant Dirac operator and real structure which satisfy these modified properties.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.04.003
Ludwik Da̧browski 1 ; Giovanni Landi 2 ; Mario Paschke 3 ; Andrzej Sitarz 4

1 Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014, Trieste, Italy
2 Dipartimento di Matematica e Informatica, Università di Trieste via A. Valerio 12/1, 34127, Trieste, Italy
3 Max-Planck-Institut für Mathematik in den Naturwissenschaften, 04103 Leipzig, Germany
4 Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland 
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     title = {The spectral geometry of the equatorial {Podle\'s} sphere},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {819--822},
     publisher = {Elsevier},
     volume = {340},
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Ludwik Da̧browski; Giovanni Landi; Mario Paschke; Andrzej Sitarz. The spectral geometry of the equatorial Podleś sphere. Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 819-822. doi : 10.1016/j.crma.2005.04.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.04.003/

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