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3-Leibniz bialgebras (3-Lie bialgebras)

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Type
Preprint
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Submission Date
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arXiv ID: 1604.04475
Source
arXiv
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Abstract

In this paper by use of cohomology complex of $3$-Leibniz algebras, the definitions of Leibniz bialgebras (and Lie bialgebras) are extended for the case of $3$-Leibniz algebras. Many theorems about Leibniz bialgebras are extended and proved for 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. $3$-Lie bialgebra as particular case of the $3$-Leibniz bialgebra is investigated. Finally, some simple examples are discussed in detail.

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