关于可分裂线性李代数的说明

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-25 DOI:10.1016/j.laa.2024.07.016

Zhiguang Hu, Haichuan Bai

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引用次数: 0

摘要

如果线性李代数包含每个元素的半纯部分和零纯部分，那么它就是可分裂的。我们很早就知道，当且仅当 g=a+n 时，一个可解线性李代数 g 是可分裂的，其中 a 是由半简单元素组成的 g 的无性子代数，n 是 g 的所有零势矩阵的理想数。此外，我们还确定了由半简单元素或零能元素组成的线性李代数的结构。

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A note on splittable linear Lie algebras

A linear Lie algebra is splittable if it contains the semisimple and nilpotent parts of each element. It is early known that a solvable linear Lie algebra $g$ is splittable if and only if $g = a + n$ , where $a$ is an abelian subalgebra of $g$ composed of semisimple elements and $n$ is the ideal of all nilpotent matrices of $g$ . In this paper, using elementary linear algebra we give a direct proof of the theorem and related results. Besides, we determine the structure of linear Lie algebras composed of semisimple or nilpotent elements.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.