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 -