Nondegenerate graded lie algebras with degenerate transitive subalgebras

被引：0
|
作者：
Gregory T.B. [1 ]
Kuznetsov M.I. [2 ]
机构：
[1] Department of Mathematics, The Ohio State University, Mansfield
[2] Nizhny Novgorod State University, Nizhny Novgorod
来源：
Journal of Mathematical Sciences | 2009年 / 161卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Minimal Ideal; Invariant Bilinear Form; Maximal Subalgebra; Bracket Operation; Recognition Theorem;
D O I：
10.1007/s10958-009-9536-6
中图分类号：
学科分类号：
摘要：
The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler is analyzed. Transitive irreducible graded Lie algebras over an algebraically closed field of characteristic p > 2 with classical reductive component L0 are considered. We show that if a nondegenerate Lie algebra L containes a transitive degenerate subalgebra L′such that dim L′1 > 1, then L is an infinite-dimensional Lie algebra. © 2009 Springer Science+Business Media, Inc.
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页码：57 / 69
页数：12
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