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The Dirac operator on SU_q(2)

Ludwik Dabrowski·Giovanni Landi·Andrzej Sitarz·Walter van Suijlekom·Joseph C. Varilly
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Abstract

We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). 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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Ludwik Dabrowski, Giovanni Landi, Andrzej Sitarz, Walter van Suijlekom, Joseph C. Varilly. 2005-02-03. The Dirac operator on SU_q(2). https://doi.org/10.1007/s00220-005-1383-9

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