对合导子构造的3-李双代数与3-Pre-李代数

白瑞蒲, 侯帅, 亢闯闯

数学学报 ›› 2020, Vol. 63 ›› Issue (2) : 123-136.

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PDF(445 KB)
数学学报 ›› 2020, Vol. 63 ›› Issue (2) : 123-136. DOI: 10.12386/A2020sxxb0010
论文

对合导子构造的3-李双代数与3-Pre-李代数

    白瑞蒲1, 侯帅2, 亢闯闯3
作者信息 +

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

    Rui Pu BAI1, Shuai HOU2, Chuang Chuang KANG3
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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.

Abstract

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

Key words

3-Lie algebra / Involutive derivation / Local cocycle 3-Lie bialgebra / 3-Lie classical Yang-Baxter equation

引用本文

导出引用
白瑞蒲, 侯帅, 亢闯闯. 对合导子构造的3-李双代数与3-Pre-李代数. 数学学报, 2020, 63(2): 123-136 https://doi.org/10.12386/A2020sxxb0010
Rui Pu BAI, Shuai HOU, Chuang Chuang KANG. 3-Lie Bialgebras and 3-pre-Lie Algebras Induced by Involutive Derivations. Acta Mathematica Sinica, Chinese Series, 2020, 63(2): 123-136 https://doi.org/10.12386/A2020sxxb0010

参考文献

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[7] Chari V., Pressley A. N., A Guide to Quantum Groups, Cambridge University Press, Cambridge, 1995:2-3.
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基金

河北省自然科学基金项目(A2018201126)

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