A Local Index Formula for the Quantum Sphere

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 εD 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.