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The Dirac Operator on SU q (2)


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.

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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.

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Dabrowski, L., Landi, G., Sitarz, A. et al. The Dirac Operator on SU q (2). Commun. Math. Phys. 259, 729–759 (2005).

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