Short $\mathrm{SL}_2$-structures on simple Lie algebras-Reference-Cited by-同舟云学术

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

Published:2023 Issue:4 Volume:214 Page:567-612
ISSN:1064-5616
Container-title:Sbornik: Mathematics
language:en
Short-container-title:Sb. Math.

Author:

Stasenko Roman Olegovich¹²

Affiliation:

1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

2. Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

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.

Funder

Russian Foundation for Basic Research

Ministry of Science and Higher Education of the Russian Federation

Publisher

Steklov Mathematical Institute

Subject

Algebra and Number Theory

Reference9 articles.

1. Non-abelian gradings of Lie algebras;E. B. Vinberg,2017

2. Short 𝑆𝑂₃-structures on simple Lie algebras and associated quasielliptic planes

3. A Structure Theory for Jordan Algebras

4. Amer. Math. Soc. Colloq. Publ.;N. Jacobson,1968

5. Structure of Lie groups and Lie algebras;A. L. Onishchik, E. B. Vinberg and V. V. Gorbatsevich,1990

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1. Short $$(\textbf{SL}_2\times \textbf{SL}_2)$$-structures on Lie algebras;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2024-01-06