局部上循环的3-Hom李双代数和3-李经典Hom-杨巴克斯方程

Local Cocycle $3$-Hom-Lie Bialgebras and $3$-Lie Classical Hom-Yang-Baxter Equation

中文关键词:  局部上循环的3-Hom李双代数  3-李Hom-杨巴克斯方程  上边缘条件

英文关键词:local cocycle $3$-Hom-Lie bialgebra  $3$-Lie CHYBE  coboundary condition

中文摘要:

      本文介绍了局部上循环的3-Hom李双代数,它的乘法和余乘两种运算的相容条件由局部上循环条件给出.作者研究了扭的3元版本的杨巴克斯方程,称为3-李Hom-杨巴克斯方程,它是文献[1]中3- 李杨巴克斯方程的一种广义化.文章证明由3-李Hom-杨巴克斯方程的解所诱导的双代数,可得到上边缘的局部上循环的3-Hom 李双代数.

英文摘要:

      In this paper, we introduce $3$-Hom-Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycle conditions. We study a twisted $3$-ary version of the Yang-Baxter Equation, called the $3$-Lie classical Hom-Yang-Baxter Equation ($3$-Lie CHYBE), which is a general form of $3$-Lie classical Yang-Baxter Equation and prove that the bialgebras induced by the solutions of $3$-Lie CHYBE induce the coboundary local cocycle $3$-Hom-Lie bialgebras.