数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (2): 513-522.doi: 10.1016/S0252-9602(14)60024-2

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3-LIE BIALGEBRAS

白瑞蒲|程宇|李佳倩|孟伟   

  1. College of Mathematics and Computer Science, Hebei University, Baoding 071002, China; Department of Mathematics, Baoding University, Baoding 071002, China; College of Mathematics and Computer Science, Hebei University, Baoding 071002, China; College of Mathematics and Computer Science, Hebei University, Baoding 071002, China  
  • 收稿日期:2012-02-27 出版日期:2014-03-20 发布日期:2014-03-20
  • 基金资助:

    The project is partially supported by NSF (11371245) of China, and NSF (A2010000194) of Hebei Province.

3-LIE BIALGEBRAS

 BAI Rui-Pu, CHENG Yu, LI Jia-Qian, MENG Wei   

  1. College of Mathematics and Computer Science, Hebei University, Baoding 071002, China; Department of Mathematics, Baoding University, Baoding 071002, China; College of Mathematics and Computer Science, Hebei University, Baoding 071002, China; College of Mathematics and Computer Science, Hebei University, Baoding 071002, China
  • Received:2012-02-27 Online:2014-03-20 Published:2014-03-20
  • Supported by:

    The project is partially supported by NSF (11371245) of China, and NSF (A2010000194) of Hebei Province.

摘要:

3-Lie algebras have close relationships with many important fields in mathemat-ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char-acteristic zero are provided.

关键词: 3-Lie algebra, 3-Lie coalgebra, 3-Lie bialgebra

Abstract:

3-Lie algebras have close relationships with many important fields in mathemat-ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char-acteristic zero are provided.

Key words: 3-Lie algebra, 3-Lie coalgebra, 3-Lie bialgebra

中图分类号: 

  • 17B05