JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

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Engel’s theorem for generalized H-Lie algebras#br#

GUO Shuang-jian1, DONG Li-hong2   

  1. 1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China;
    2. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, China
  • Received:2013-06-05 Online:2014-04-20 Published:2014-06-03

Abstract: It is studied that the representation of the Lie algebras in the Yetter-Drinfel’d category HH YD(i.e. generalized H-Lie algebras). The Engel’s theorem for generalized H-Lie algebras is proved: Let L be a generalized H-Lie algebra, if every cyclic Yetter-Drinfel’d submodule of L is ad-nilpotent, then L is nilpotent.

Key words: Generalized H-Lie algebra, Engel’s theorem, Yetter-Drinfel’d category

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