Hom-Lie 2代数的构造  

The construction of Hom-Lie 2-algebras

作　　者：韩铎 江卫华[1] HAN Duo;JIANG Weihua(School of Sciences,Tibet University,850000,Lhasa,Xizang,PRC)

机构地区：[1]西藏大学理学院,西藏自治区拉萨市850000

出　　处：《曲阜师范大学学报(自然科学版)》2025年第2期49-58,共10页Journal of Qufu Normal University(Natural Science)

基　　金：西藏自治区自然科学基金(XZ202501ZR0116).

摘　　要：该文研究了如何构造Hom-Lie 2代数.首先,依据Hom-Lie 2代数的概念,介绍了从Hom-Leibniz代数构造出Hom-Lie 2代数的方法.在此基础上,介绍了如何从2个Hom-Leibniz代数的张量积、Hom-dialgebra、Hom-Leibniz代数和交换Hom-dialgebra的张量积、Hom-associative代数和Hom-Omni-Lie代数构造出Hom-Leibniz代数,从而构造出Hom-Lie 2代数.另外,介绍了如何从2个Hom-dialgebra的张量积构造出Hom-dialgebra和如何从Hom-dendriform代数构造出Hom-associative代数,从而构造出Hom-Lie 2代数.最后,介绍了利用Rota-Baxter算子从Rota-Baxter Hom-Lie代数构造出Hom-Lie 2代数的方法.How to construct Hom-Lie 2-algebras was studied.First,based on the notion of Hom-Lie 2-algebras,the construction of Hom-Lie 2-algebras from Hom-Leibniz algebras was introduced emphatically.On this basis,the construction of Hom-Leibniz algebras from the tensor product of two Hom-Leibniz algebras,Hom-dialgebras,tensor product of Hom-Leibniz algebras and commutative Hom-dialgebras,Hom-associative algebras and Hom-Omni-Lie algebras was given separately so as to achieve the goal of the construction of Hom-Lie 2-algebras.In addition,how to construct Hom-dialgebras from tensor product of two Hom-dialgebras and how to construct Hom-associative algebras from Hom-dendriform algebras were introduced separately in order to obtain Hom-Lie 2-algebras.At last,the construction of Hom-Lie 2-algebras from Rota-Baxter Hom-Lie algebras through Rota-Baxter operator was introduced.

关 键 词：Hom-Lie 2代数 Hom-Leibniz代数 构造 

分 类 号：O152.5[理学—数学]