Letters in Mathematical Physics

, Volume 75, Issue 3, pp 235–254

Local Index Formula on the Equatorial Podleś Sphere

Authors

  • Francesco D’andrea
    • Scuola Internazionale Superiore di Studi Avanzati
    • Scuola Internazionale Superiore di Studi Avanzati
Article

DOI: 10.1007/s11005-005-0047-1

Cite this article as:
D’andrea, F. & Da̧browski, L. Lett Math Phys (2006) 75: 235. doi:10.1007/s11005-005-0047-1
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Abstract

We discuss spectral properties of the equatorial Podleś sphere Sq2. As a preparation we also study the ‘degenerate’ (i.e. q=0) case (related to the quantum disk). Over Sq2 we consider two different spectral triples:one related to the Fock representation of the Toeplitz algebra and the isopectral one given in [7]. After the identification of the smooth pre-C*-algebra we compute the dimension spectrum and residues. We check the nontriviality of the (noncommutative) Chern character of the associated Fredholm modules by computing the pairing with the fundamental projector of the C*-algebra (the nontrivial generator of the K0-group) as well as the pairing with the q-analogue of the Bott projector. Finally, we show that the local index formula is trivially satisfied.

Mathematics Subject Classifications (2000).

Primary 58B34Secondary 17B37

Keywords

Noncommutative geometryspectral triplequantum sphere
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© Springer 2006