Hopf structure in nambu-lien-algebras

Muradian, R.; Santana, A. E.

doi:10.1007/bf02557108

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Cited by 4 publications

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“…In this manner, the generalization of the concept of Lie bialgebra to the n-Lie bialgebra (in general) and especially 3-Lie bialgebra is a good problem from the abstract point of view. Indeed, there are some attempts in this direction from the co-algebra point of view (see [13] and [14]). Here we will study these facts by use of the cohomology of n-Leibniz algebra [5] for 3-Leibniz algebra in general and then for 3-Lie algebra in particular 1 .…”

Section: Introductionmentioning

confidence: 99%

3-Leibniz bialgebras (3-Lie bialgebras)

Rezaei-Aghdam

Sedghi-Ghadim

2017

Int. J. Geom. Methods Mod. Phys.

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The aim of this paper is to extend the notion of bialgebra for Leibniz algebras (and Lie algebras) to 3-Leibniz algebras (and 3-Lie algebras) by use of the cohomology complex of 3-Leibniz algebras. Also, some theorems about Leibniz bialgebras are extended and proved in the case of 3-Leibniz bialgebras (3-Lie bialgebras). Moreover, a new theorem on the correspondence between 3-Leibniz bialgebra and its associated Leibniz bialgebra is proved. Finally, some examples are discussed in detail.

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Section: Introductionmentioning

confidence: 99%