On Lie gradings II

Abstract

To obtain fine gradings of gl( n, C), it is necessary to study maximal Abelian subgroups (MAD-subgroups) of diagonizable automorphisms in A ut(gl( n, C)). We described two finite sets H n and K n such that each MAD-subgroup consisting only from inner automorphisms is conjugated to some element of H n and each MAD-subgroup containing at least one outer automorphism is conjugated to some element of K n . Using these results concerning K n we then easily find all MAD-subgroups in A ut(o( n, C)) for n ⊄ 8 and in A ut(sp(2 n, C)).