Abstract
For a given abelian group G, we classify the isomorphism classes of Ggradings on the simple restricted Lie algebras of types W.mI1/ and S.mI1/ for m 2, in terms of numerical and group-theoretical invariants. Our main tool is automorphism group schemes, which we determine for the simple restricted Lie algebras of types S.mI1/ and H.mI1/. The ground field is assumed to be algebraically closed of characteristic p > 3.
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