ON LIE GRADINGS-II

To obtain fine gradings of gl(iz, C), it is necessary to study maximal Abelian subgroups (MAD-subgroups) of diagonizable automorphisms in Au t(gl(n, C)). We described two finite sets H-n and H-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 o uter automorphism is conjugated to some-element of H-n. Using these re sults concerning H-n,, we then easily find all MAD-subgroups in Aut(o( n, C)) for n not equal 8 and in Aut(sp(2n, C)). (C) 1998 Elsevier Scie nce :Inc, All rights reserved.