The Dirac operator on SU_q(2)

Details The Dirac operator on SU_q(2) The Dirac operator on SU_q(2)

2004-11-27

arxiv.org/abs/math/0411609v2

Commun.Math.Phys. 259 (2005) 729-759

Mathematics

Quantum Algebra

v2: minor changes; to appear in CMP

Scientific paper

10.1007/s00220-005-1383-9

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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