8-维3-李代数的Manin Triple

doi:10.6040/j.issn.1671-9352.0.2018.196

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (6): 30-33.doi: 10.6040/j.issn.1671-9352.0.2018.196

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8-维3-李代数的Manin Triple

白瑞蒲^1,2,吴婴丽^1,2,侯帅^1,2

1.河北大学数学与信息科学学院, 河北保定 071002;2. 河北省机器学习与计算智能重点实验室, 河北保定 071002

发布日期:2019-06-05
作者简介:白瑞蒲(1960— ),女,博士,教授,主要从事李代数、多元代数的研究. E-mail:bairuipu@hbu.edu.cn
基金资助:
河北省自然科学基金资助项目(A2018201126)

8-dimensional Manin Triple of 3-Lie algebras

BAI Rui-pu^1,2, WU Ying-li^1,2, HOU Shuai^1,2

1. College of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei, China;
2. Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, Baoding 071002, Hebei, China

Published:2019-06-05

摘要/Abstract

摘要： 利用对合导子及伴随表示的对偶模构造了对偶3-李代数,证明了特征为0的代数闭域上任意4-维3-李代数存在对合导子,并利用4-维3-李代数的对合导子构造了7种不同构的8-维 3-李代数的Manin Triple。

关键词: 3-李代数, 对合导子, Manin Triple

Abstract: Dual 3-Lie algebras are constructed by involutive derivations and dual modules. It is proved that there exist involutive derivations on 4-dimensional 3-Lie algebras over an algebraically closed field of characteristic zero, and by the involutive derivations on 4-dimensional 3-Lie algebras, seven non-isomorphic 8-dimensional Manian Triples of 3-Lie algebras are constructed.

Key words: 3-Lie algebra, involutive derivation, Manin Triple

中图分类号:

O152.5

白瑞蒲,吴婴丽,侯帅. 8-维3-李代数的Manin Triple[J]. 《山东大学学报(理学版)》, 2019, 54(6): 30-33.

BAI Rui-pu, WU Ying-li, HOU Shuai. 8-dimensional Manin Triple of 3-Lie algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 30-33.

参考文献

[1] FILIPPOV V T. n-Lie algebras[J]. Siberian Mathematical Journal, 1985, 26(6):879-891. doi:10.1007/bf00969110.
[2] BAI Ruipu, BAI Chengming, WANG Jinxiu. Realizations of 3-Lie algebras[J]. Journal of Mathematical Physics, 2010, 51(6):063505. doi:10.1063/1.3436555.
[3] BAI Ruipu. LI Zhenheng,WANG Weidong. Infinite-dimensional 3-Lie algebras and their connections to Harish-Chandra modules[J]. Frontiers of Mathematics in China, 2017, 12(3):515-530. doi:10.1007/s11464-017-0606-7.
[4] BAI Chengming, GUO Li, SHENG Yunhe. Bialgebras, the classical Yang-Baxter equation and main triples for 3-Lie algebras[J/OL]. arXiv:1604.05996v1[math-ph].
[5] BAI Ruipu, SONG Guojie, ZHANG Yaozhong. On classification of n-Lie algebras[J]. Frontiers of Mathematics in China, 2011, 6(4):581-606.

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8-维3-李代数的Manin Triple

8-dimensional Manin Triple of 3-Lie algebras

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