2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67431We describe a general technique to study Dirac operators on noncommutative spaces under some additional assumptions. The main idea is to capture the compact resolvent condition in a combinatorial set up. Using this, we then prove that for a certain class of representations of the C^*-algebra C(SU_q(\ell+1)), any Dirac operator that diagonalises with respect to the natural basis of the underlying Hilbert space must have trivial sign.v3: partly rewritten; the equivariant case has now been taken out and would be treated in a separate paper. v2: few typos corrected. LaTeX2e, uses xy-pic and eepicOperator AlgebrasCombinatoricsQuantum Algebra58B34, 46L87, 19K33text