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 Uq(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.

The Dirac operator on SUq(2)

LANDI, GIOVANNI;
2005

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 Uq(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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/1695870
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