2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185765We analize the role of GL_2, a quantum group constructed by Dipper-Donkin, as a global symmetry for quantum chains, and show the way to construct all possible Hamiltonians for four states quantum chains with GL_2 global symmetry. In doing this, we search all inner actions of GL_2 on the Clifford algebra C(1,3) and show them. We also introduce the corresponding operator algebras, invariants and Hamiltonians, explicitly.30 pages, 3 Figures, LaTex2eQuantum AlgebraHigh Energy Physics - Theorytext