Projections of Semisimple Lie Algebras

被引：0
|
作者：
Gein, A. G. [1 ]
机构：
[1] Eltsin Ural Fed Univ, Ul Mira 19, Ekaterinburg 620002, Russia
来源：
ALGEBRA AND LOGIC | 2019年 / 58卷 / 02期
关键词：
subalgebra lattice; lattice isomorphism; semisimple Lie algebras; modular subalgebra; LATTICES;
D O I：
10.1007/s10469-019-09529-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is proved that the property of being a semisimple algebra is preserved under projections (lattice isomorphisms) for locally finite-dimensional Lie algebras over a perfect field of characteristic not equal to 2 and 3, except for the projection of a three-dimensional simple nonsplit algebra. Over fields with the same restrictions, we give a lattice characterization of a three-dimensional simple split Lie algebra and a direct product of a one-dimensional algebra and a three-dimensional simple nonsplit one.
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收藏
页码：103 / 114
页数：12
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