From the Albert algebra to Kac's ten-dimensional Jordan superalgebra via tensor categories in characteristic 5

Elduque, Alberto (Universidad de Zaragoza) ; Etingof, Pavel ; Kannan, Arun S.

Resumen: Kac’s ten-dimensional simple Jordan superalgebra over analgebraically closed field of characteristic 5 is obtained froma process of semisimplification, via tensor categories, fromthe exceptional simple Jordan algebra (or Albert algebra),together with a suitable order 5 automorphism.This explains McCrimmon’s ‘bizarre result’ asserting that,in characteristic 5, Kac’s superalgebra is a sort of ‘degree 3Jordan superalgebra’.As an outcome, the exceptional simple Lie superalgebrael(5; 5), specific of characteristic 5, is obtained from the simpleLie algebra of type E8 and an order 5 automorphism.In the process, precise recipes to obtain superalgebras fromalgebras in Rep Cp (or Rep αp), p > 2, are given

Idioma: Inglés

DOI: 10.1016/j.jalgebra.2024.12.006

Año: 2024

Publicado en: Journal of Algebra 666 (2024), 387-414
ISSN: 0021-8693

Factor impacto JCR: 0.8 (2024)

Categ. JCR: MATHEMATICS rank: 193 / 483 = 0.4 (2024) - Q2 - T2

Factor impacto SCIMAGO: 1.029 - Algebra and Number Theory (Q1)

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

Tipo y forma: Article (Published version)

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