Journal of Jilin University Science Edition ›› 2020, Vol. 58 ›› Issue (5): 1073-1078.

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Structure of a Class of Non-Abelian n-Lie Algebras

BAI Ruipu, WU Yingli   

  1. College of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei Province, China
  • Received:2020-02-17 Online:2020-09-26 Published:2020-11-18

Abstract: We studied the structure of non-Abelian n-Lie algebras with β(L)=m-n+1, and classified n-Lie algebras that satisfied dim L1<4. We  prove that there are only 2,6 and 11 classes in the cases dimL1=1,2,3, respectively. Furthermore, if β(L)=m-n+1 and  Z(L)L1, then (m-n+1)/2≤dimL1≤m-n+1.

Key words: n-Lie algebra, maximal Abelian ideal, derived algebra

CLC Number: 

  • O152.5