Higher-dimensional general Jacobi identities I
Loading...
Date
2017
Authors
ORCID
Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
Altmetrics
Abstract
It 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.
Description
Citation
Mathematics for Applications. 2017 vol. 6, č. 1, s. 43-98. ISSN 1805-3629
http://ma.fme.vutbr.cz/archiv/6_1/ma_6_1_nishimura_final.pdf
http://ma.fme.vutbr.cz/archiv/6_1/ma_6_1_nishimura_final.pdf
Document type
Peer-reviewed
Document version
Published version
Date of access to the full text
Language of document
en
Study field
Comittee
Date of acceptance
Defence
Result of defence
Document licence
© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky