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arXiv · 2110.03826

Hom-Leibniz bialgebras and BiHom-Leibniz dendriform algebras

Ismail Laraiedh·Sergei Silvestrov
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Abstract

The notion of a Hom-Leibniz bialgebra is introduced and it is shown that matched pairs of Hom-Leibniz algebras, Manin triples of Hom-Leibniz algebras and Hom-Leibniz bialgebras are equivalent in a certain sense. The notion of Hom-Leibniz dendriform algebra is established, their bimodules and matched pairs are defined and their properties and theorems about their interplay and construction are obtained. Furthermore, the concept of BiHom-Leibniz dendriform algebras is introduced and discussed, their bimodules and matched pairs are constructed and properties are described. Finally, the connections between all these algebraic structures using $\mathcal{O}$-operators are shown.

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Ismail Laraiedh, Sergei Silvestrov. 2021-10-07. Hom-Leibniz bialgebras and BiHom-Leibniz dendriform algebras. https://arxiv.org/abs/2110.03826

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