2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65117We construct quantum commutators on module-algebras of quasi-triangular Hopf algebras. These are quantum-group covariant, and have generalized antisymmetry and Leibniz properties. If the Hopf algebra is triangular they additionally satisfy a generalized Jacobi identity, turning the module-algebra into a quantum-Lie algebra.LaTeX 2e (uses AMS styles), 10 pages, no figuresQuantum AlgebraMathematical Physics16W30; 16W10; 17D99text