2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143953We discuss the consistency of the axioms which the definition of quantum Lie algebras is usually based on.Talk, given by D.Gurevich at the Satellite Conference "From Lie algebras to quantum groups", Coimbra (Portugal), Juin 2006. To be published in the Proceedings of the Conference. Some essential typos in macrocommands were correctedQuantum Algebra17B37; 81R50text