Short (SL2 x SL2)-structures on Lie algebras

Beites, Patricia D. ; Córdova-Martínez, Alejandra S. ; Cunha, Isabel ; Elduque, Alberto (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1007/s13398-023-01541-4

Año: 2024

Publicado en: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 118 (2024), 45 [21 pp.]
ISSN: 1578-7303

Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2021-123461NB-C22
Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-20R
Financiación: info:eu-repo/grantAgreement/ES/DGA/S60-20R
Financiación: info:eu-repo/grantAgreement/ES/MCINN/PID2021-123461NB-C21

Tipo y forma: Article (Published version)

Área (Departamento): Área Algebra (Dpto. Matemáticas)