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

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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

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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
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