I am wondering if an extension of Noether theorem to supergroups exists. In particular the analogy with the usual case should be that supersymmmetries are in 1-to-1 correspondence to certain "currents" whose charge is the supersymmetric spinor charge $Q_{\alpha}$.
Has this topic been studied at all?
I) First it should be stressed that Noether's theorem is not really about Lie groups but only about Lie algebras, i.e., one just needs $n$ infinitesimal symmetries to deduce $n$ conservation laws.
II) Secondly, it is straightforward to check (by recalling the proof of Noether's theorem) that Noether's theorem generalizes to supernumber-valued variables, transformations, currents, and charges.
Examples of Grassmann-odd symmetries include BRST symmetry and Poincare super-symmetry.
