2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63021We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L_2-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p<4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L_2-space.LaTeX2e, 19 pages; v3:some results added in existing sections, one new section on classical SU(2) added, two references added; v2:some typos and one error correctedK-Theory and HomologyOperator AlgebrasQuantum Algebra46L87, 19K33, 81R50text