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Lie algebras generated by extremal elements

Arjeh M. Cohen·Anja Steinbach·Rosane Ushirobira·David B. Wales
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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 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.

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Arjeh M. Cohen, Anja Steinbach, Rosane Ushirobira, David B. Wales. 1999-03-12. Lie algebras generated by extremal elements. https://arxiv.org/abs/math/9903077

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