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A geometrical interpretation of Okubo spin group

2022-02-21Journal article Restricted access
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dc.contributor.authorCorradetti, Daniele
dc.contributor.authorZucconi, Francesco
dc.date.accessioned2023-01-14T11:22:24Z
dc.date.available2023-01-14T11:22:24Z
dc.date.issued2022-02-21
dc.description.abstractIn this work we define, for the first time, the affine and projective plane over the real Okubo algebra, showing a concrete geometrical interpretation of its Spin group. Okubo algebra is a flexible, composition algebra which is also a not unital division algebra. Even though Okubo algebra has been known for more than 40 years, we believe that this is the first time the algebra was used for affine and projective geometry. After showing that all axioms of affine geometry are verified, we define a projective plane over Okubo algebra as completion of the affine plane and directly through the use of Veronese coordinates. We then present a bijection between the two constructions. Finally we show a geometric interpretation of Spin(O) as the group of collineations that preserve the axis of the plane.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1016/j.geomphys.2022.104641pt_PT
dc.identifier.eissn1879-1662
dc.identifier.urihttp://hdl.handle.net/10400.1/18813
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.subjectOkubo algebrapt_PT
dc.subjectProjective planept_PT
dc.subjectSping grouppt_PT
dc.subjectSymmetric compositionpt_PT
dc.subjectCollineationpt_PT
dc.subjectVeronesept_PT
dc.titleA geometrical interpretation of Okubo spin grouppt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.startPage104641pt_PT
oaire.citation.titleJournal of Geometry and Physicspt_PT
oaire.citation.volume182pt_PT
person.familyNameCorradetti
person.givenNameDaniele
person.identifier.orcid0000-0001-8086-0593
rcaap.rightsrestrictedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublicationeb033bd7-b864-44d6-8c79-e64b25bb2b6e
relation.isAuthorOfPublication.latestForDiscoveryeb033bd7-b864-44d6-8c79-e64b25bb2b6e

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