2023/03/31 by Patrícia Damas Beites, Beites, Patricia D., Alejandra S. Córdova-Martínez +5 · 1 citation
Mathematics · #17B70 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2303.17993
openalex publication_date 2023/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
S-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 (SL2xSL2)-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.