2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224750We study a twisted version of the Yang-Baxter Equation, called the Hom-Yang-Baxter Equation (HYBE), which is motivated by Hom-Lie algebras. Three classes of solutions of the HYBE are constructed, one from Hom-Lie algebras and the others from Drinfeld's (dual) quasi-triangular bialgebras. Each solution of the HYBE can be extended to operators that satisfy the braid relations. Assuming an invertibility condition, these operators give a representation of the braid group.11 pages, to appear in Journal of Physics AMathematical PhysicsQuantum AlgebraRings and Algebras16W30, 17A30, 17B37, 81R50text