余芳, 毕艳会, 张涛. 非交换omni-李2-代数[J]. 南昌航空大学学报(自然科学版), 2024, 38(3): 72-77. DOI: 10.3969/j.issn.2096-8566.2024.03.007
引用本文: 余芳, 毕艳会, 张涛. 非交换omni-李2-代数[J]. 南昌航空大学学报(自然科学版), 2024, 38(3): 72-77. DOI: 10.3969/j.issn.2096-8566.2024.03.007
Fang YU, Yan-hui BI, Tao ZHANG. Non-abelian Omni-Lie 2-algebras[J]. Journal of nanchang hangkong university(Natural science edition), 2024, 38(3): 72-77. DOI: 10.3969/j.issn.2096-8566.2024.03.007
Citation: Fang YU, Yan-hui BI, Tao ZHANG. Non-abelian Omni-Lie 2-algebras[J]. Journal of nanchang hangkong university(Natural science edition), 2024, 38(3): 72-77. DOI: 10.3969/j.issn.2096-8566.2024.03.007

非交换omni-李2-代数

Non-abelian Omni-Lie 2-algebras

  • 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(\textG) \oplus \textG 上定义 \textG -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 \textG -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。

     

    Abstract: In this paper, we study the structure of non-abelian omni-Lie 2-algebras. Firstly, we define a \textG -valued pairing and a bracket operation on the direct sum space gl(\textG) \oplus \textG 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.

     

/

返回文章
返回