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Lie algebras generated by extremal elements

Cohen, Arjeh M. and Steinbach, Anja and Ushirobira, Rosane and Wales, David (1999) Lie algebras generated by extremal elements. . (Unpublished)

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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.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20191009-092215716
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99180
Deposited By: Tony Diaz
Deposited On:09 Oct 2019 17:39
Last Modified:02 Jun 2023 01:30

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