2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209869We study the canonical basis for the negative part of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras associated to two different matrices satisfying certain conditions may coincide. We show that the canonical bases coincide provided that the algebras coincide. We also answer partially a question by Lusztig.To appear in Nagoya Math JRepresentation TheoryQuantum Algebra17B37, 16G20, 14L30text