Simple Lie algebras having extremal elements

A.M. Cohen, G. Ivanyos, D.A. Roozemond

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)

Abstract

Let L be a simple finite-dimensional Lie algebra of characteristic distinct from 2 and from 3. Suppose that L contains an extremal element that is not a sandwich, that is, an element x such that [x, [x, L]] is equal to the linear span of x in L. In this paper we prove that, with a single exception, L is generated by extremal elements. The result is known, at least for most characteristics, but the proofs in the literature are involved. The current proof closes a gap in a geometric proof that every simple Lie algebra containing no sandwiches (that is, ad-nilpotent elements of order 2) is in fact of classical type.
Original languageEnglish
Pages (from-to)177-188
JournalIndagationes Mathematicae. New Series
Volume19
Issue number2
DOIs
Publication statusPublished - 2008

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