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Orthogonal Gyrodecompositions of Real Inner Product Gyrogroups

2020-06-03Journal article Open access
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dc.contributor.authorFerreira, Milton
dc.contributor.authorSuksumran, Teerapong
dc.date.accessioned2020-07-15T13:11:52Z
dc.date.available2020-07-15T13:11:52Z
dc.date.issued2020-06-03
dc.description.abstractIn this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, M\"{o}bius, Proper Velocity, and Chen's gyrogroups. This leads to the study of left (right) coset partition of a real inner product gyrogroup induced from a subgyrogroup that is a finite dimensional subspace. As~a result, we obtain gyroprojectors onto the subgyrogroup and its orthogonal complement. We~construct also quotient spaces and prove an associated isomorphism theorem. The left (right) cosets are characterized using gyrolines (cogyrolines) together with automorphisms of the subgyrogroup. With~the algebraic structure of the decompositions, we study fiber bundles and sections inherited by the gyroprojectors. Finally, the general theory is exemplified for the aforementioned gyrogroups.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationFerreira, M.; Suksumran, T. Orthogonal Gyrodecompositions of Real Inner Product Gyrogroups. Symmetry 2020, 12(6), 941.pt_PT
dc.identifier.doi10.3390/sym12060941pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.8/5008
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherMDPIpt_PT
dc.relationFCT - Fundação para a Ciência e a Tecnologia, projeto UIDB/04106/2020pt_PT
dc.relationCentro de Pesquisa em Matemática e Matemática Aplicada da Universidade de Chiang Maipt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectReal inner product gyrogrouppt_PT
dc.subjectOrthogonal decompositionpt_PT
dc.subjectGyroprojectionpt_PT
dc.subjectCoset spacept_PT
dc.subjectPartitionspt_PT
dc.subjectQuotient spacept_PT
dc.subjectGyrolinespt_PT
dc.subjectCogyrolinespt_PT
dc.subjectfiber bundlespt_PT
dc.titleOrthogonal Gyrodecompositions of Real Inner Product Gyrogroupspt_PT
dc.title.alternativeReceived: 6 May 2020; Accepted: 30 May 2020; Published: datept_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage36pt_PT
oaire.citation.issue6pt_PT
oaire.citation.startPage1pt_PT
oaire.citation.titleSymmetrypt_PT
oaire.citation.volume12pt_PT
person.familyNameFerreira
person.givenNameMilton
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.orcid0000-0003-1816-8293
person.identifier.ridA-2004-2015
person.identifier.scopus-author-id12144179800
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublicationb1460cdc-4ced-46c6-a637-68b425d104dc
relation.isAuthorOfPublication.latestForDiscoveryb1460cdc-4ced-46c6-a637-68b425d104dc

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