QUANTIZATIONS OF POISSON LIE GROUPS AS NONCOMMUTATIVE MANIFOLDS

On any q-deformation of a simply connected simple compact Poisson Lie group we construct; an equivariant spectral triple which is an isospectral deformation of that defined by the Dirac operator on the original group. Our quantum Dirac operator is defined using a Drinfeld twist which relates the q-deformed compact quantum group to the original group, and thus a priori depends on the choice of the twist, but it turns out that the spectral triple is nevertheless unique up to unitary equivalence.