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