Short $\mathrm{SL}_2$-structures on simple Lie algebras

IF 0.8 4区数学 Q2 MATHEMATICS Sbornik Mathematics Pub Date : 2023-01-01 DOI:10.4213/sm9788e

Roman Olegovich Stasenko

引用次数: 0

Abstract

In Vinberg's works certain non-Abelian gradings of simple Lie algebras were introduced and investigated, namely, short $\mathrm{SO}_3$- and $\mathrm{SL}_3$-structures. We investigate a different kind of these, short $\mathrm{SL}_2$-structures. The main results refer to the one-to-one correspondence between such structures and certain special Jordan algebras. Bibliography: 8 titles.

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简单李代数上的短$\ mathm {SL}_2$-结构

在Vinberg的著作中，引入并研究了简单李代数的非阿贝尔分级，即短$\mathrm{SO}_3$-和$\mathrm{SL}_3$-结构。我们研究了一种不同的$\ mathm {SL}_2$-结构。主要结果是这种结构与某些特殊的约当代数之间的一一对应关系。参考书目:8篇。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis

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