2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70116We prove some relations for the $q$-multiple zeta values ($q$MZV). They are $q$-analogues of the cyclic sum formula, the Ohno relation and the Ohno-Zagier relation for the multiple zeta values (MZV). We discuss the problem to determine the dimension of the space spanned by $q$MZV's over $\Q$, and present an application to MZV.16 pagesQuantum AlgebraNumber Theory05A30, 11B65, 33D15text