Higher-dimensional general Jacobi identities I

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dc.contributor.authorNishimura, H.
dc.coverage.issue1cs
dc.coverage.volume6cs
dc.date.accessioned2019-01-02T12:37:01Z
dc.date.available2019-01-02T12:37:01Z
dc.date.issued2017cs
dc.description.abstractIt was shown by the author [International Journal of Theoretical Physics 36 (1997), 1099{1131] that what is called the general Jacobi identity, obtaining in microcubes, underlies the Jacobi identity of vector elds. It is well known in the theory of Lie algebras that a plethora of higher-dimensional generalizations of the Jacobi identity hold, though they are usually established not as a derivation on the nose from the axioms of Lie algebras but by making an appeal to the socalled Poincar e{Birkho {Witt theorem and the like. The general Jacobi identity was rediscovered by Kirill Mackenzie in the second decade of this century [Geometric Methods in Physics, Birkh auser/Springer, 2013, 357{366]. The principal objective of this paper is to investigate a four-dimensional generalization of the general Jacobi identity in detail. In a subsequent paper we will propose a uniform method for establishing a bevy of higher-dimensional generalizations of the general Jacobi identity under a single umbrella.en
dc.formattextcs
dc.format.extent43-98cs
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMathematics for Applications. 2017 vol. 6, č. 1, s. 43-98. ISSN 1805-3629cs
dc.identifier.doi10.13164/ma.2017.05en
dc.identifier.issn1805-3629
dc.identifier.urihttp://hdl.handle.net/11012/137254
dc.language.isoencs
dc.publisherVysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematikycs
dc.relation.ispartofMathematics for Applicationsen
dc.relation.urihttp://ma.fme.vutbr.cz/archiv/6_1/ma_6_1_nishimura_final.pdfcs
dc.rights© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematikycs
dc.rights.accessopenAccessen
dc.subjectgeneral Jacobi identityen
dc.subjectsynthetic di erential geometryen
dc.subjectFr olicher{Nijenhuis calculusen
dc.titleHigher-dimensional general Jacobi identities Ien
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
eprints.affiliatedInstitution.departmentÚstav matematikycs
eprints.affiliatedInstitution.facultyFakulta strojního inženýrstvícs
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