Lie algebras generated by extremal elements
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2007-05-23 v1 代数几何
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摘要
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.
引用
@article{arxiv.math/9903077,
title = {Lie algebras generated by extremal elements},
author = {Arjeh M. Cohen and Anja Steinbach and Rosane Ushirobira and David B. Wales},
journal= {arXiv preprint arXiv:math/9903077},
year = {2007}
}
备注
28 pages