Leibniz Bialgebras, Classical Yang-Baxter Equations and Dynamical Systems

被引：3

作者：

Rezaei-Aghdam, Adel ^{[1
]}

Sedghi-Ghadim, Leila ^{[2
]}

Haghighatdoost, Ghorbanali ^{[1
,2
]}

机构：

[1] Azarbaijan Shahid Madani Univ, Dept Phys, Tabriz 51745406, Iran

[2] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz 51745406, Iran

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2021年 / 31卷 / 05期

关键词：

Coboundary Leibniz bialgebra; Leibniz algebra; Leibniz(Lie) bialgebra; Yang-Baxter equation; ALGEBRAS;

D O I：

10.1007/s00006-021-01177-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：20

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