Automorphisms and twisted forms of generalized Witt Lie algebras

Author:
William C. Waterhouse

Journal:
Trans. Amer. Math. Soc. **327** (1991), 185-200

MSC:
Primary 17B40; Secondary 17B50

MathSciNet review:
1038018

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Abstract: We prove that the automorphisms of the generalized Witt Lie algebras over arbitrary commutative rings of characteristic all come from automorphisms of the algebras on which they are defined as derivations. By descent theory, this result then implies that if a Lie algebra over a field becomes isomorphic to over the algebraic closure, it is a derivation algebra of the type studied long ago by Ree. Furthermore, all isomorphisms of those derivation algebras are induced by isomorphisms of their underlying associative algebras.

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DOI:
https://doi.org/10.1090/S0002-9947-1991-1038018-X

Article copyright:
© Copyright 1991
American Mathematical Society