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Abstract
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This work is intended as an attempt to extend the notion
of bialgebra for Lie algebras to Leibniz algebras and also, the correspondence between the Leibniz bialgebras and its dual is investigated.
Moreover, the coboundary Leibniz bialgebras, the classical r-matrices,
and Yang–Baxter equations related to the Leibniz algebras are defined,
and some examples are given. Finally, a method for the construction
of a dynamical system on a Leibniz manifold via Leibniz bialgebra is
presented.
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