Beites, Patrícia DamasCórdova Martínez, Alejandra SarinaCunha, IsabelElduque, Alberto2026-01-202026-01-202024-01-06Beites, P.D., Córdova-Martínez, A.S., Cunha, I. et al. Short -structures on Lie algebras. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 45 (2024). https://doi.org/10.1007/s13398-023-01541-41578-7303http://hdl.handle.net/10400.6/19699S-structures on Lie algebras, introduced by Vinberg, represent a broad generalization of the notion of gradings by abelian groups. Gradings by, not necessarily reduced, root systems provide many examples of natural S-structures. Here we deal with a situation not covered by these gradings: the short (SL2 × SL2)-structures, where the reductive group is the simplest semisimple but not simple reductive group. The algebraic objects that coordinatize these structures are the J -ternary algebras of Allison, endowed with a nontrivial idempotent.engS-structuresJ -ternary álgebrasStructurable algebrasjournal article10.1007/s13398-023-01541-41579-1505