, Volume 259, Issue 3, pp 729-759
Date: 21 Jun 2005

The Dirac Operator on SU q (2)

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Abstract

We construct a 3+-summable spectral triple over the quantum group SU q (2) which is equivariant with respect to a left and a right action of The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.

Communicated by A. Connes
Partially supported by Polish State Committee for Scientific Research (KBN) under grant 2 P03B 022 25.
Regular Associate of the Abdus Salam ICTP, Trieste.