2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122598The quantum group $SU_q(\ell+1)$ has a canonical action on the odd dimensional sphere $S_q^{2\ell+1}$. All odd spectral triples acting on the $L_2$ space of $S_q^{2\ell+1}$ and equivariant under this action have been characterized. This characterization then leads to the construction of an optimum family of equivariant spectral triples having nontrivial $K$-homology class. These generalize the results of Chakraborty & Pal for $SU_q(2)$.LaTeX2e, 20 pagesQuantum AlgebraK-Theory and HomologyOperator Algebras58B34, 46L87, 19K33text