Equivariant spectral triples and Poincaré duality for SUq(2)

Let A be the C-algebra associated with SUq(2), π be the representation by left multiplication on the L2 space of the Haar state and let D be the equivariant Dirac operator for this representation constructed by the authors earlier. We prove in this article that there is no operator other than the scalars in the commutant π(A) that has bounded commutator with D. This implies that the equivariant spectral triple under consideration does not admit a rational Poincaré dual in the sense of Moscovici, which in particular means that this spectral triple does not extend to a K-homology fundamental class for SUq(2). We also show that a minor modification of this equivariant spectral triple gives a fundamental class and thus implements Poincaré duality. AMS Subject Classification No.: 58B34, 46L87, 19K33