The Dirac Operator on SUq(2) |
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| Authors: | Ludwik Dabrowski Giovanni Landi Andrzej Sitarz Walter van Suijlekom Joseph C. Várilly |
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| Affiliation: | (1) Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014 Trieste, Italy;(2) Dipartimento di Matematica e Informatica, Università di Trieste, Via Valerio 12/b, 34127 Trieste;(3) INFN, Sezione di Napoli, Napoli, Italy;(4) Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland;(5) Departamento de Matemática, Universidad de Costa Rica, 2060, San José, Costa Rica |
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| Abstract: | We construct a 3+-summable spectral triple  over the quantum group SUq(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.Partially supported by Polish State Committee for Scientific Research (KBN) under grant 2 P03B 022 25.Regular Associate of the Abdus Salam ICTP, Trieste. |
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