Theoretical algebraic analysis characterizes extended Rota-Baxter Leibniz bialgebras through Manin triples and matched pairs, highlighting new solutions to the classical Leibniz Yang-Baxter equation.
In this paper, we first introduce the notions of extended Leibniz-dendriform algebras and extended post-Leibniz algebras, and investigate their intrinsic relationship with extended Rota-Baxter Leibniz algebras. Next, we propose the concepts of extended Rota-Baxter Leibniz bialgebras and admissible quadruples of extended Rota-Baxter Leibniz algebras. Furthermore, we define the Manin triple and the matched pair of extended Rota-Baxter Leibniz algebras. We then prove that extended Rota-Baxter Leibniz bialgebras can be equivalently characterized by matched pairs and Manin triples of extended Rota-Baxter Leibniz algebras. Finally, we construct several classes of extended Rota-Baxter Leibniz bialgebras via the admissible classical Leibniz Yang-Baxter equation (cLYBe) and 𝒪-operators.
No takes yet. Share an insight, caveat, or question.
Li et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: