3-Leibniz bialgebras (3-Lie bialgebras)

Abstract

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.

28 pages

References in corpus (6)

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Cited by in corpus (4)

• Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and O-operators
• From Basu-Harvey to Nahm equation via 3-Lie bialgebra
• M2 to D2 and vice versa by 3-Lie and Lie bialgebra
• 3-Leibniz bialgebra in $N=6$ Chern-Simons gauge theories, multiple M2 to D2 branes and vice versa