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Outer Derivations and Classical-Albert-Zassenhaus lie Algebras

Published online by Cambridge University Press:  20 November 2018

David J. Winter
David J. Winter*
Affiliation:
University of Michigan, Ann Arbor, Michigan
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This paper is concerned with the structure of the derivation algebra Der L of the Lie algebra L with split Cartan subalgebra H. The Fitting decomposition

of Der L with respect to ad ad H leads to a decomposition

where

This decomposition is studied in detail in Section 2, where the centralizer of ad L∞ in D0(H) is shown to be

which is Hom(L/L2, Center L) when H is Abelian. When the root-spaces La (a nonzero) are one-dimensional, this leads to the decomposition of Der L as

where T is any maximal torus of D0(H).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 6 , 01 December 1984 , pp. 961 - 972
Copyright
Copyright © Canadian Mathematical Society 1984

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