Nijenhuis Operators on n-Lie Algebras

In this paper, we study（n-1）-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various construc...

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Published inCommunications in theoretical physics Vol. 65; no. 6; pp. 659 - 670
Main Author 刘杰锋 生云鹤 周彦秋 白承铭
Format Journal Article
LanguageEnglish
Published 01.06.2016
Subjects
Algebra
Construction
Deformation
Operators (mathematics)
Polynomials
s算子
Theoretical physics
代数阶
小变形
李代数
算子多项式
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Summary:In this paper, we study（n-1）-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples.
Bibliography:Nijenhuis operators n-Lie algebras deformations Rota–Baxter operators
Jie-Feng Liu, Yun-He Sheng , Yan-Qiu Zhou , Cheng-Ming Bai （1.Department of Mathematics, Xinyang Normal University, Xinyang 464000, China; 2.Department of Mathematics, Jilin University, Changchun 130012, China; 3.Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China）
11-2592/O3
In this paper, we study（n-1）-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples.
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/65/6/659