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Bounded and unbounded Fredholm modules for quantum projective spaces

Published online by Cambridge University Press:  16 February 2010

Francesco D'Andrea  and
Giovanni Landi
Francesco D'Andrea
Affiliation:
Département de Mathématique, Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348, Louvain-La-Neuve, Belgium, [email protected]
Giovanni Landi
Affiliation:
Dipartimento di Matematica e Informatica, Università di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy and INFN, Sezione di Trieste, Trieste, Italy, [email protected]
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Abstract

We construct explicit generators of the K-theory and K-homology of the coordinate algebras of ‘functions’ on the quantum projective spaces. We also sketch a construction of unbounded Fredholm modules, that is to say Diraclike operators and spectral triples of any positive real dimension.

Keywords

Noncommutative geometryFredholm modulesquantum projective spaces
Type
Research Article
Information
Journal of K-Theory , Volume 6 , Issue 2 , October 2010 , pp. 231 - 240
Copyright
Copyright © ISOPP 2010

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References

1.Cuntz, J., “On the homotopy groups for the space of endomorphisms of a C*-algebra”, in: Operator Algebras and Group Representations, Pitman, London, 1984, pp. 124–137.Google Scholar
2.D'Andrea, F. and Dąbrowski, L., Local Index Formula on the Equatorial Podleś Sphere, Lett. Math. Phys. 75 (3) (2006), 235–254; [arxiv:math/0507337].Google Scholar
3.D'Andrea, F. and Dąbrowski, L., Dirac operators on Quantum Projective Spaces, preprint [arxiv:0901.4735], 2009.Google Scholar
4.D'Andrea, F., Dąbrowski, L., Landi, G., and Wagner, E., Dirac operators on all Podleś spheres, J. Noncomm. Geom. 1 (2) (2007), 213–239; [arxiv:math/0606480].Google Scholar
5.D'Andrea, F. and Landi, G., Antiself-dual Connections on the Quantum Projective Plane: Monopoles, [arxiv:0903.3551], 2009.Google Scholar
6.Hawkins, E. and Landi, G., Fredholm Modules for Quantum Euclidean Spheres, J. Geom. Phys. 49 (3-4) (2004), 272–293; [arxiv:math/0210139].Google Scholar
7.Hong, J.H. and Szymański, W., Quantum Spheres and Projective Spaces as Graph Algebras, Commun. Math. Phys. 232 (2002), 157–188.CrossRefGoogle Scholar
8.Vaksman, L. and Soibelman, Ya., The algebra of functions on the quantum group SU(n + 1) and odd-dimensional quantum spheres, Leningrad Math. J. 2 (1991), 1023–1042.Google Scholar