2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78786We introduce the tangent space $ T({\rm H}_q) $ on the quantum hyperboloid ($ {\cal A}_{0,q}^c $) and equip it with an action on $ {\cal A}_{0,q}^c $ being a deformation of the action of vectors fields on functions. An embedding $ \displaystyle sl(2)_q \longrightarrow T({\rm H}_q) $ of $q$-deformed Lie algebra $ sl(2) $ being an analogue of the anchor $ \displaystyle sl(2) \longrightarrow \Vect({\rm H}) $ is called "quantum anchor".7 pages Latex. To appear in Proceedings of whorkshop on Hopf algebras (1998) at VUB (Belgium)Quantum Algebratext