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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

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 $ W(m,{\mathbf{n}})$ over arbitrary commutative rings of characteristic $ p \geq 3$ 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 $ W(m,{\mathbf{n}})$ 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: http://dx.doi.org/10.1090/S0002-9947-1991-1038018-X
PII: S 0002-9947(1991)1038018-X
Article copyright: © Copyright 1991 American Mathematical Society