Affiliation:
1. School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, P. R. China
2. School of Mathematics and Statistics, Yili Normal University, Yining 835000, P. R. China
Abstract
In this paper, we re-establish a bialgebraic theory on a Hom–Leibniz algebra by a new dual representation, which weakens the involutive condition on the structure map in [S. Guo, S. X. Wang and X. H. Zhang, The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras, Mathematics 10 (2022) 1920; I. Laraiedh and S. Silvestrov, Hom–Leibniz bialgebras and BiHom–Leibniz dendriform algebras, Afr. Mat. 34 (2023), Article ID: 28, 45 pp]. We also give the classification of triangular Hom–Leibniz bialgebras on two-dimensional Hom–Leibniz algebras induced by “Yau twist principle”.
Funder
Natural Science Foundation of Henan Province
University Science Program Project of Xinjiang
Publisher
World Scientific Pub Co Pte Ltd