对合导子构造的3-李双代数与3-Pre-李代数  

3-Lie Bialgebras and 3-pre-Lie Algebras Induced by Involutive Derivations

作　　者：白瑞蒲[1] 侯帅 亢闯闯 Rui Pu BAI;Shuai HOU;Chuang Chuang KANG(College of Mathematics and Information Science,Hebei University,Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province,Baoding 071002,P.R.China;School of Mathematics,Jilin University,Changchun 130012,P.R.China;School of Mathematics,Nankai University,Tianjin 30071,P.R.China)

机构地区：[1]河北大学数学与信息科学学院河北省机器学习与智能计算重点实验室,保定071002 [2]吉林大学数学科学学院,长春130012 [3]南开大学数学科学学院,天津300071

出　　处：《数学学报（中文版）》2020年第2期123-136,共14页Acta Mathematica Sinica：Chinese Series

基　　金：河北省自然科学基金项目(A2018201126)。

摘　　要：研究具有对合导子的3-李代数的结构,证明了具有对合导子的m-维3-李代数A存在相容的3-Pre-李代数,且在2m-维半直积3-李代数Aad*A*上存在局部上循环3-李双代数结构.利用对合导子构造了3-李代数Aad*A*上的3-李Yang-Baxter方程的解和一类3-Pre-李代数,并构造了8-维和10-维局部上循环3-李双代数.We studied the structure of 3-Lie algebras with involutive derivations,and proved that if A is an m-dimensional 3-Lie algebra with an involutive derivation,then there exists a compatible 3-pre-Lie algebra and a local cocycle 3-Lie bialgebraic structure on the 2m-dimensional semi-direct product 3-Lie algebra Aad*A*.By means of involutive derivations,we constructed the skew-symmetric solution of the 3-Lie classical Yang-Baxter equation in the 3-Lie algebra Aad*A*,a class of 3-pre-Lie algebras,and eight and ten dimensional local cocycle 3-Lie bialgebras.

关 键 词：3-李代数 对合导子 局部上循环3-李双代数 3-李Yang-Baxter方程 

分 类 号：O152.5[理学—数学]