Geodesic
Lie Algebras with Nilpotent Centralizers
Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 929-941

Voir la notice de l'article provenant de la source Cambridge University Press

We consider finite dimensional Lie algebras over an algebraically closed field F of arbitrary characteristic. Such an algebra L will be called a centralizer nilpotent Lie algebra (abbreviated c.n.) provided that the centralizer C(x) is a nilpotent subalgebra of L for all nonzero x ∈ L.For each algebraically closed F, there is a unique simple Lie algebra of dimension 3 over F which we shall denote S(F). This algebra has a basis e −1, e 0, e 1 such that [e −1e 0] = e −1, [e −1e 1] = e 0 and [e 0e 1] = e 1. (If char(F) ≠ 2, then S(F) ≅ sl 2(F).) It is trivial to check that S(F) is a c.n. algebra for all F.There are two other types of simple Lie algebras we consider. If char (F) = 3, construct the octonion (Cayley) algebra over F. 
Benkart, G. M.; Isaacs, I. M. Lie Algebras with Nilpotent Centralizers. Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 929-941. doi: 10.4153/CJM-1979-088-8
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