具有给定子代数与元素性质的李代数
环与代数
2014-08-14 v3
摘要
本文给出了特征零域上有限维李代数的下列几类结果：迷向李代数（即每个伴随算子均为半单算子的李代数）、正则李代数（即在布尔巴基意义下每个非零元均为正则元的李代数）、极小非交换李代数（即所有真子代数均为交换代数的非交换李代数）以及深度为2的李代数（即所有真子代数均为交换或极小非交换的李代数）。
引用
@article{arxiv.1105.4284,
title = {Lie algebras with given properties of subalgebras and elements},
author = {Pasha Zusmanovich},
journal= {arXiv preprint arXiv:1105.4284},
year = {2014}
}
备注
8 pages; v3: added proofs; fixed a list of algebras of depth 2 in Theorem 7; the statement of Theorem 5 is weakened, the former statement added as conjecture; to appear in Proceedings of the Conference "Algebra - Geometry - Mathematical Physics" (Mulhouse, 2011), Springer Proc. Math. Stat