Dynamical Symmetries for Graded Vector Fields. Issue 2 (3rd July 2019) - Azizpour, Esmaeil; Atayi, Dordi Mohammad
Abstract: Suppose that = ( M, M ) is a graded manifold and consider a direct subsheaf of Der M and a graded vector field Γ on ; both satisfying certain conditions. We associate to the graded vector field Γ ∈ Der M, a set of 1-forms and show that if φ ∈ is a non-degenerate graded 1-form and X ∈ Der M such that for some superfunction f on, then the superfunction F = f − J ( φ )( X ) satisfies . This result, generalizes the conditions under which there exist a solution for the inverse problem.