On strongly inert subalgebras of an infinite-dimensional Lie algebra

被引：0
|
作者：
Petravchuk A.P. [1 ]
机构：
[1] Kiev University, Kiev
来源：
Ukrainian Mathematical Journal | 2002年 / 54卷 / 7期
关键词：
Arbitrary Field; Local Finiteness;
D O I：
10.1023/A:1022043215520
中图分类号：
学科分类号：
摘要：
We study infinite-dimensional Lie algebras L over an arbitrary field that contain a subalgebra A such that dim (A + [A, L])/A < ∞. We prove that if an algebra L is locally finite, then the subalgebra A is contained in a certain ideal I of the Lie algebra L such that dimI/A < ∞. We show that the condition of local finiteness of L is essential in this statement. © 2002 Plenum Publishing Corporation.
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页码：1234 / 1238
页数：4
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