From octonions to composition superalgebras via tensor categories

Daza-García, Alberto ; Elduque, Alberto (Universidad de Zaragoza) ; Sayin, Umut

Resumen: The nontrivial unital composition superalgebras, of dimension 3 and 6, which exist only in characteristic 3, are obtained from the split Cayley algebra and its order 3 automorphisms, by means of the process of semisimplification of the symmetric tensor category of representations of the cyclic group of order 3. Connections with the extended Freudenthal magic square in characteristic 3, that contains some exceptional Lie superalgebras specific of this characteristic are discussed too. In the process, precise recipes to go from (nonassociative) algebras in this tensor category to the corresponding superalgebras are given.

Idioma: Inglés

DOI: 10.4171/RMI/1408

Año: 2024

Publicado en: REVISTA MATEMATICA IBEROAMERICANA 40, 1 (2024), 129-152
ISSN: 0213-2230

Financiación: info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-P
Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-20R
Financiación: info:eu-repo/grantAgreement/ES/MCINN/PID2021-123461NB-C21
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PRE2018-087018

Tipo y forma: Article (Published version)

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