2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58385We construct the general supersymmetry algebra via the adjoint action on a semi-Hopf algebra which has a more general structure than a Hopf algebra. As a result we have an extended supersymmetry theory with quantum gauge group, i.e., quantised enveloping algebra of a simple Lie algebra. For the example, we construct the N=1 and generalized N=2 supersymmetry theory which leads to the Seiberg-Witten theory.16 pages, no figureMathematical PhysicsQuantum Algebratext