The Dirac operator on SU_q(2)

Dabrowski, Ludwik; Landi, Giovanni; Sitarz, Andrzej; Van Suijlekom, Walter; Várilly Boyle, Joseph C.

The Dirac operator on SU_q(2)

Archivos

Naiad.pdf (318.83 KB)

Fecha

2005

Tipo

artículo original

Autores

Dabrowski, Ludwik

Landi, Giovanni

Sitarz, Andrzej

Van Suijlekom, Walter

Várilly Boyle, Joseph C.

Resumen

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.