Throughout the papers of E.B. Vinberg some non-abelian gradings of simple Lie algebras were introduced and investigated, namely short $SO_3 -$ and $SL_3$ - structures. We study another kind of them -- short $SL_2$ - structures. The main results relate to one-to-one corresponding between such structures and some special Jordan algebras.
On the irreducibility of irreducible characters of simple Lie algebras
Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras
Structure constants for simple Lie algebras from principal $\mathfrak{sl}_2$-triple
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