2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56216We define a semi-Hopf algebra which is more general than a Hopf algebra. Then we construct the supersymmetry algebra via the adjoint action on this semi-Hopf algebra. As a result we have a supersymmetry theory with quantum gauge group, i.e., quantised enveloping algebra of a simple Lie algebra. For the example, we construct the Lagrangian N=1 and N=2 supersymmetry.15 pages, no figure and typos correctedHigh Energy Physics - TheoryMathematical PhysicsQuantum Algebratext