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 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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https://hal.archives-ouvertes.fr/hal-00438549
Contributor : Rosane Ushirobira <>
Submitted on : Thursday, December 3, 2009 - 11:46:00 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

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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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