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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?

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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.

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