JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 30-33.doi: 10.6040/j.issn.1671-9352.0.2018.196

Previous Articles    

8-dimensional Manin Triple of 3-Lie algebras

BAI Rui-pu1,2, WU Ying-li1,2, HOU Shuai1,2   

  1. 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

PDF (PC)

436

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

CLC Number: 

  • O152.5
[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.
[1] LI Qiang, MA Li-li, WANG Xiao-yan, LYU Li-jiao. Abelian extensions of Hom-Jordan Lie algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 4-8.
[2] GONG Ben-xue and LI Sha-sha . Realization of O(Spq(4)) arising from Uq(sp(4)) via the Jantzen approach [J]. J4, 2007, 42(8): 91-94 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd