2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118082In this paper, we introduce the notion of abstract crystals for quantum generalized Kac-Moody algebras and study their fundamental properties. We then prove the crystal embedding theorem and give a characterization of the crystals $B(\infty)$ and $B(\la)$.20 pagesQuantum AlgebraRepresentation Theory81R50,17B37text