2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69810We describe the crystal bases of modified quantum algebras and its connected component containing ``zero vector''by the polyhedral realization method for the types A_n and A^(1)_1. We also present the explicit form of the unique highest weight vector in the connected component.22 pages, LaTeXQuantum AlgebraRepresentation Theorytext