From octonions to composition superalgebras via tensor categories

Alberto Daza-García ^[1] ; Alberto Elduque ^[1] ; Umut Sayin ^[2]
1. [1] Universidad de Zaragoza
  
  Universidad de Zaragoza
  
  Zaragoza, España
2. [2] Duzce University
  
  Duzce University
  
  Turquía
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 1, 2024, págs. 129-152
Idioma: inglés
DOI: 10.4171/RMI/1408
Enlaces
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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.