From octonions to composition superalgebras via tensor categories

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dc.authoridSayin, Umut/0000-0003-3648-1881en_US
dc.authoridDaza-Garcia, Alberto/0000-0002-6438-802Xen_US
dc.authorscopusid57219312842en_US
dc.authorscopusid7003818649en_US
dc.authorscopusid57209736240en_US
dc.authorwosidSayin, Umut/HGB-7576-2022en_US
dc.contributor.authorDaza-Garcia, Alberto
dc.contributor.authorElduque, Alberto
dc.contributor.authorSayin, Umut
dc.date.accessioned2024-08-23T16:03:28Z
dc.date.available2024-08-23T16:03:28Z
dc.date.issued2024en_US
dc.departmentDüzce Üniversitesien_US
dc.description.abstractThe 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.en_US
dc.description.sponsorshipAEI/FEDER, UE; MCIN/AEI [E22_20R]; ERDF A way of making Europe; Gobierno de Aragon, Grupo de investigacion Algebra y Geometria [MTM2017-83506-C2-1-P]; FPI grant; TUBITAK 2219; [PID2021-123461NB-C21]; [PRE2018-087018]en_US
dc.description.sponsorshipThe first two authors have been supported by grant MTM2017-83506-C2-1-P (AEI/FEDER, UE) , by grant PID2021-123461NB-C21, funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe, and by grant E22_20R (Gobierno de Aragon, Grupo de investigacion Algebra y Geometria) . The first author also acknowledges support by the FPI grant PRE2018-087018. The third author has been supported by grant TUBITAK 2219.en_US
dc.identifier.doi10.4171/RMI/1408
dc.identifier.endpage152en_US
dc.identifier.issn0213-2230
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85187010175en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage129en_US
dc.identifier.urihttps://doi.org/10.4171/RMI/1408
dc.identifier.urihttps://hdl.handle.net/20.500.12684/13767
dc.identifier.volume40en_US
dc.identifier.wosWOS:001168226500001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherEuropean Mathematical Soc-Emsen_US
dc.relation.ispartofRevista Matematica Iberoamericanaen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectoctonionsen_US
dc.subjectsuperalgebrasen_US
dc.subjecttensor categoryen_US
dc.subjectsemisimplificationen_US
dc.subjectVerlinde categoryen_US
dc.subjectMagic Squareen_US
dc.titleFrom octonions to composition superalgebras via tensor categoriesen_US
dc.typeArticleen_US

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