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Simple Lie Algebras of Witt Type

✍ Scribed by D.S. Passman

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 149 KB
Volume: 206
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7444

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✦ Synopsis

Let K be a field, let A be an associative, commutative K-algebra, and let ⌬ be a nonzero K-vector space of commuting K-derivations of A. Then, with a rather natural definition, A m ⌬ s A⌬ becomes a Lie algebra and we obtain necessary K and sufficient conditions here for this Lie algebra to be simple. With one minor exception in characteristic 2, simplicity occurs if and only if A is ⌬-simple and A ⌬ m ⌬ s A ⌬ ⌬ acts faithfully as derivations on A.

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