非交换omni-李2-代数  

Non-abelian Omni-Lie 2-algebras

作　　者：余芳 毕艳会[1] 张涛[2] YU Fang;BI Yan-hui;ZHANG Tao(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China;College of Mathematics and Information Science,Henan Normal University,Xinxiang Henan 453007,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063 [2]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《南昌航空大学学报（自然科学版）》2024年第3期72-77,共6页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(11961049,11601219);江西省自然科学基金重点项目(20232ACB201004)。

摘　　要：本文对非交换omni-李2-代数结构进行研究。首先,在直和空间gl(G)⊕G上定义G-值配对和括号运算,构造非交换omni-李2-代数,并证明它是一个严格的Leibniz 2-代数。其次,证明非交换omni-李2-代数的括号与G-值配对是相容的,具有omni-李2-代数类似的性质。最后,构造omni-李2-代数上的Nijenhuis算子,证明非交换omni-李2-代数可以看成omni-李2-代数的平凡形变。In this paper,we study the structure of non-abelian omni-Lie 2-algebras.Firstly,we define a G-valued pairing and a gl(G)⊕Gbracket operation on the direct sum space such that a non-abelian omni-Lie 2-algebra is constructed.At the same time,we prove that it is a strict Leibniz 2-algebra.Secondly,we prove that the bracket is compatible with the symmetric pairing and their properties are similar to the properties of omni-Lie 2-algebras.Lastly,a Nijenhuis operator on Leibniz 2-algebras is constructed,and it is shown that a non-abelian omni-Lie 2-algebra can be considered as a trivial deformation of an omni-Lie 2-algebra.

关 键 词：非交换omni-李2-代数 平凡形变 严格李2-代数 非交换 

分 类 号：O154.2[理学—数学]