Classification of group gradings on simple Lie algebras of types A, B, C and D

For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple Lie algebras of types An (n⩾1), Bn (n⩾2), Cn (n⩾3) and Dn (n>4), in terms of numerical and group-theoretical invariants. The ground field is assumed to be algebraically closed of characteristic different from 2.