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The Dirac operator on SU_q(2)

TitleThe Dirac operator on SU_q(2)
Publication TypeJournal Article
Year of Publication2005
AuthorsDabrowski, L, Landi, G, Sitarz, A, van Suijlekom, W, Varilly, JC
JournalCommun. Math. Phys. 259 (2005) 729-759

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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