R. O. Stasenko, “Short <nobr>$\mathrm{SL}_2$</nobr>-structures on simple Lie algebras”, Mat. Sb., 2023, Volume 214, Number 4,Pages <nobr>132

This article is cited in 2 papers

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

R. O. Stasenko^ab

^a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b 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.

Keywords: Jordan algebras, structured Lie algebras, graded Lie algebras.

MSC: Primary 17B70; Secondary 17B25, 17C40

Received: 04.05.2022 and 24.12.2022

DOI: 10.4213/sm9788