2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53741We construct the space of vector fields on quantum groups . Its elements are products of the known left invariant vector fields with the elements of the quantum group itself. We also study the duality between vector fields and 1-forms. The construction is easily generalized to tensor fields. A Lie derivative along any (also non left invariant) vector field is proposed. These results hold for a generic Hopf algebra.LATEX FILE,16 pages November 1993 UCLA/93/TEP/25High Energy Physics - Theorytext