Lie algebras generated by extremal elements

We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals) over a field of characteristic distinct from 2. There is an associative bilinear form on such a Lie algebra; we study its connections with the Killing form. Any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal numbers of extremal generators for the Lie algebras of type A(n) (n greater than or equal to 1), B-n (n greater than or equal to 3), C-n (n greater than or equal to 2), D-n (n greater than or equal to 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. (C) 2001 Academic Press.