The spectral geometry of the equatorial Podleś sphere

Ludwik Da̧browski; Giovanni Landi; Mario Paschke; Andrzej Sitarz

doi:10.1016/j.crma.2005.04.003

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 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

Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 819-822.

Résumé
Abstract

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 $U_{q} (su (2))$ -equivariant Dirac operator and real structure which satisfy these modified properties.

Reçu le : 2004-09-20
Accepté le : 2005-03-29
Publié le : 2005-05-17

DOI : 10.1016/j.crma.2005.04.003

Affiliations des auteurs :

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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     author = {Ludwik Da̧browski and Giovanni Landi and Mario Paschke and Andrzej Sitarz},
     title = {The spectral geometry of the equatorial {Podle\'s} sphere},
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     pages = {819--822},
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     language = {en},
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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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