English

A Local Index Formula for the Quantum Sphere

Quantum Algebra 2007-05-23 v2 Operator Algebras

Abstract

For the Dirac operator D on the standard quantum sphere we obtain an asymptotic expansion of the SU_q(2)-equivariant entire cyclic cocycle corresponding to \epsilon D when evaluated on the element k^2\in U_q(su_2). The constant term of this expansion is a twisted cyclic cocycle which up to a scalar coincides with the volume form and computes the quantum as well as the classical Fredholm indices.

Cite

@article{arxiv.math/0309275,
  title  = {A Local Index Formula for the Quantum Sphere},
  author = {Sergey Neshveyev and Lars Tuset},
  journal= {arXiv preprint arXiv:math/0309275},
  year   = {2007}
}

Comments

17 pages; minor corrections, references added