Symmetries Of The Super Dirac Hierarchy And Its Lie Algebra

In this paper, the symmetries and its Lie algebra structure of the super Dirac hierarchy and super AKNS hierarchy are discussed. First, we find that the recursion operator0of the hierarchy is a strong hereditary symmetry. From this,2N2families of symmetries and their infinite-dimensional Lie algebra structure are proposed. By contrast the symmetries and Lie algebra structure with these of general Dirac hierarchy, we find that the intro-ducing of super variables have no influence. Furthermore, the super AKNS hierarchy and general AKNS hierarchy also have the same form of symmetries and Lie algebra structure.