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NS-Leibniz bialgebras, the Yang--Baxter equation and relative Rota--Baxter operators
We introduce NS-Leibniz bialgebras and establish their equivalence with matched pairs and Manin triples of NS-Leibniz algebras. In the coboundary case, skew-symmetric solutions of the NS-Leibniz Yang--Baxter equation yield NS-Leibniz bialgebras and correspond to $\mathcal{O}$-operators for the dual
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