Lie algebras generated by extremal elements - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 1999

Lie algebras generated by extremal elements

Arjeh M. Cohen
  • Fonction : Auteur
Anja Steinbach
  • Fonction : Auteur
David B. Wales
  • Fonction : Auteur

Résumé

We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.

Dates et versions

hal-00438549 , version 1 (03-12-2009)

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Arjeh M. Cohen, Anja Steinbach, Rosane Ushirobira, David B. Wales. Lie algebras generated by extremal elements. 1999. ⟨hal-00438549⟩
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