From octonions to composition superalgebras via tensor categories
Küçük Resim Yok
Tarih
2024
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
European Mathematical Soc-Ems
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
octonions, superalgebras, tensor category, semisimplification, Verlinde category, Magic Square
Kaynak
Revista Matematica Iberoamericana
WoS Q Değeri
N/A
Scopus Q Değeri
Q1
Cilt
40
Sayı
1
