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dc.contributor.authorMcInroy, Justin
dc.contributor.authorShpectorov, Sergey
dc.date.accessioned2022-07-28T12:53:31Z
dc.date.available2022-07-28T12:53:31Z
dc.date.issued2021-12-22
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/627049/split%20spin%20factor.pdf?sequence=1
dc.identifier.citationMcInroy, J., & Shpectorov, S. (2022). Split spin factor algebras. Journal of Algebra, 595, 380–397. https://doi.org/10.1016/j.jalgebra.2021.12.022en_US
dc.identifier.issn0021-8693
dc.identifier.doi10.1016/j.jalgebra.2021.12.022
dc.identifier.urihttp://hdl.handle.net/10034/627049
dc.description.abstractMotivated by Yabe's classification of symmetric $2$-generated axial algebras of Monster type \cite{yabe}, we introduce a large class of algebras of Monster type $(\alpha, \frac{1}{2})$, generalising Yabe's $\mathrm{III}(\alpha,\frac{1}{2}, \delta)$ family. Our algebras bear a striking similarity with Jordan spin factor algebras with the difference being that we asymmetrically split the identity as a sum of two idempotents. We investigate the properties of these algebras, including the existence of a Frobenius form and ideals. In the $2$-generated case, where our algebra is isomorphic to one of Yabe's examples, we use our new viewpoint to identify the axet, that is, the closure of the two generating axes.en_US
dc.publisherElsevieren_US
dc.relation.urlhttps://www.sciencedirect.com/science/article/abs/pii/S0021869321006268?via%3Dihuben_US
dc.relation.urlhttps://research-information.bris.ac.uk/en/publications/split-spin-factor-algebras
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.subjectSpin factoren_US
dc.subjectJordan algebraen_US
dc.subjectaxial algebraen_US
dc.titleSplit spin factor algebrasen_US
dc.typeArticleen_US
dc.contributor.departmentUniversity of Bristol; Heilbronn Institute for Mathematical Research, Bristol; University of Birmingham; University of Chesteren_US
dc.identifier.journalJournal of Algebraen_US
or.grant.openaccessYesen_US
rioxxterms.funderunfundeden_US
rioxxterms.identifier.projectunfundeden_US
rioxxterms.versionAMen_US
rioxxterms.versionofrecord10.1016/j.jalgebra.2021.12.022en_US
rioxxterms.licenseref.startdate2023-12-22
dcterms.dateAccepted2021-12-17
rioxxterms.publicationdate2021-12-22
dc.date.deposited2022-07-28en_US
dc.indentifier.issn0021-8693en_US


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