Geodesic
Short $\mathrm{SL}_2$-structures on simple Lie algebras
Sbornik. Mathematics, Tome 214 (2023) no. 4, pp. 567-612

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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: structured Lie algebras, graded Lie algebras.
Mots-clés : Jordan algebras 
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     title = {Short $\mathrm{SL}_2$-structures on simple {Lie} algebras},
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R. O. Stasenko. Short $\mathrm{SL}_2$-structures on simple Lie algebras. Sbornik. Mathematics, Tome 214 (2023) no. 4, pp. 567-612. http://geodesic.mathdoc.fr/item/SM_2023_214_4_a4/