TY - JOUR

T1 - Simple Lie algebras having extremal elements

AU - Cohen, A.M.

AU - Ivanyos, G.

AU - Roozemond, D.A.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

U2 - 10.1016/S0019-3577(09)00003-2

DO - 10.1016/S0019-3577(09)00003-2

M3 - Article

SN - 0023-3358

VL - 19

SP - 177

EP - 188

JO - Indagationes Mathematicae. New Series

JF - Indagationes Mathematicae. New Series

IS - 2

ER -