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
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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.