Local Index Formula on the Equatorial Podles Sphere

Details Local Index Formula on the Equatorial Podles Sphere Local Index Formula on the Equatorial Podles Sphere

2005-07-16

arxiv.org/abs/math/0507337v3

Lett. Math. Phys. 75 (2006) 235-254

Mathematics

Quantum Algebra

18 pages, no figures; minor corrections

Scientific paper

10.1007/s11005-005-0047-1

We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one. 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 $K_0$-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.

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