实数域R上n+1维n-Lie代数的内导子代数

Inner Derivation Aglebras of(n+1)-dimensional n-Lie Agebras over the Real Field R

研究了实数域R上的n+1维n-Lie代数的分类,并讨论了R上n+1维n-Lie代数的内导子代数.特别地,得出R上单n+1维n-Lie代数的内导子代数有3种情形:Bm,Dm,Lorents李代数.

Authors mainly study the classation of （n ＋ 1）-dimensional n-Lie algebras over the real field R, and discuss its inner derivation algebras. In particular, we obtain that the inner derivation algebras of simple （ n ＋ 1）-dimensional n-Lie algebra are Bm, Dm, and Lorents Lie algebra.