On Lie gradings II

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...

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Bibliographic Details
Published in:Linear algebra and its applications 1998-06, Vol.277 (1), p.97-125
Main Authors: Havlícek, Miloslav, Patera, Jiří, Pelantova, Edita
Format: Article
Language:English
Subjects:
Automorphism
Classical Lie algebra
Gradlings
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Summary: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)).
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(97)10039-8