Lie algebras generated by extremal elements

Abstract

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 A_n (n≥1), B_n (n≥3), C_n (n≥2), D_n (n≥4), E_n (n = 6, 7, 8), F_4 and G_2 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.