2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78137For bicovariant differential calculi on quantum matrix groups a generalisation of classical notions such as metric tensor, Hodge operator, codifferential and Laplace-Beltrami operator for arbitrary k-forms is given. Under some technical assumptions it is proved that Woronowicz' external algebra of left-invariant differential forms either contains a unique form of maximal degree or it is infinite dimensional. Using Jucys-Murphy elements of the Hecke algebra the eigenvalues of the Laplace-Beltrami operator for the Hopf algebra O(SLq(N)) are computed.30 pages, LaTeX2eQuantum AlgebraMathematical PhysicsDifferential Geometry17B37, 58A14, 81R50text