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 -equivariant Dirac operator and real structure which satisfy these modified properties.
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.
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Ludwik Da̧browski 1; Giovanni Landi 2; Mario Paschke 3; Andrzej Sitarz 4
@article{CRMATH_2005__340_11_819_0, author = {Ludwik Da̧browski and Giovanni Landi and Mario Paschke and Andrzej Sitarz}, title = {The spectral geometry of the equatorial {Podle\'s} sphere}, journal = {Comptes Rendus. Math\'ematique}, pages = {819--822}, publisher = {Elsevier}, volume = {340}, number = {11}, year = {2005}, doi = {10.1016/j.crma.2005.04.003}, language = {en}, }
TY - JOUR AU - Ludwik Da̧browski AU - Giovanni Landi AU - Mario Paschke AU - Andrzej Sitarz TI - The spectral geometry of the equatorial Podleś sphere JO - Comptes Rendus. Mathématique PY - 2005 SP - 819 EP - 822 VL - 340 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2005.04.003 LA - en ID - CRMATH_2005__340_11_819_0 ER -
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/
[1] Quantum geometry of algebra factorisations and coalgebra bundles, Commun. Math. Phys., Volume 213 (2000), pp. 491-521
[2] Equivariant spectral triples on the quantum group, K-Theory, Volume 28 (2003), pp. 107-126
[3] Gravity coupled with matter and the foundation of noncommutative geometry, Comm. Math. Phys., Volume 182 (1996), pp. 155-176
[4] Cyclic cohomology, quantum group symmetries and the local index formula for , J. Inst. Math. Jussieu, Volume 3 (2004), pp. 17-68
[5] Noncommutative manifolds, the instanton algebra and isospectral deformations, Comm. Math. Phys., Volume 221 (2001), pp. 141-159
[6] L. Da̧browski, G. Landi, A. Sitarz, W. van Suijlekom, J.C. Varilly, The Dirac operator on , Comm. Math. Phys., in press
[7] Dirac operator on the standard Podles quantum sphere, Banach Center Publ., Volume 61 (2003), pp. 49-58
[8] Dirac operators on quantum flag manifolds, Lett. Math. Phys., Volume 67 (2004), pp. 49-59
[9] G. Landi, M. Paschke, A. Sitarz, unpublished notes, 1999
[10] Foundations of Quantum Group Theory, Cambridge University Press, Cambridge, 1995
[11] A local index formula for the quantum sphere | arXiv
[12] M. Paschke, Über nichtkommutative Geometrien, ihre Symmetrien und etwas Hochenergiephysik, Thesis, Mainz, 2001
[13] Quantum spheres, Lett. Math. Phys., Volume 14 (1987), pp. 521-531
[14] Dirac operator and a twisted cyclic cocycle on the standard Podles quantum sphere | arXiv
[15] Operator representation of cross product algebras of Podles quantum spheres | arXiv
[16] Equivariant spectral triples, Banach Center Publ., Volume 61 (2003), pp. 231-263
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