000133389 001__ 133389 000133389 005__ 20240926114322.0 000133389 0247_ $$2doi$$a10.4171/RMI/1408 000133389 0248_ $$2sideral$$a138088 000133389 037__ $$aART-2024-138088 000133389 041__ $$aeng 000133389 100__ $$aDaza-García, Alberto 000133389 245__ $$aFrom octonions to composition superalgebras via tensor categories 000133389 260__ $$c2024 000133389 5060_ $$aAccess copy available to the general public$$fUnrestricted 000133389 5203_ $$aThe 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. 000133389 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/PRE2018-087018$$9info:eu-repo/grantAgreement/ES/MCINN/PID2021-123461NB-C21$$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-P 000133389 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000133389 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000133389 700__ $$0(orcid)0000-0002-6497-2162$$aElduque, Alberto$$uUniversidad de Zaragoza 000133389 700__ $$aSayin, Umut 000133389 7102_ $$12006$$2005$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Algebra 000133389 773__ $$g40, 1 (2024), 129-152$$pRev. mat. iberoam.$$tREVISTA MATEMATICA IBEROAMERICANA$$x0213-2230 000133389 8564_ $$s542007$$uhttps://zaguan.unizar.es/record/133389/files/texto_completo.pdf$$yVersión publicada 000133389 8564_ $$s1299572$$uhttps://zaguan.unizar.es/record/133389/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000133389 909CO $$ooai:zaguan.unizar.es:133389$$particulos$$pdriver 000133389 951__ $$a2024-09-26-11:42:34 000133389 980__ $$aARTICLE