  We 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.
