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Leibniz Bialgebras, Classical Yang–Baxter Equations and Dynamical Systems
Advances in Applied Clifford Algebras ( IF 1.5 ) Pub Date : 2021-10-26 , DOI: 10.1007/s00006-021-01177-w
Adel Rezaei-Aghdam 1 , Ghorbanali Haghighatdoost 1, 2 , Leila Sedghi-Ghadim 2
Affiliation  

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.



中文翻译:

莱布尼茨双代数、经典杨-巴克斯特方程和动力系统

这项工作旨在尝试将李代数的双代数概念扩展到莱布尼茨代数,并且还研究了莱布尼茨双代数与其对偶之间的对应关系。此外,定义了与莱布尼茨代数相关的共边界莱布尼茨双代数、经典r矩阵和杨-巴克斯特方程,并给出了一些例子。最后,提出了一种通过莱布尼茨双代数在莱布尼茨流形上构造动力系统的方法。

更新日期:2021-10-27
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