研究了n+1维n-Lie代数的一些性质,证明了当dim[A,…,A]>1时,A的Cartan子代数的维数是n-1,且证明了n+2维n-Lie代数A是单的当且仅当A不含1维理想且A=[A,…,A]及关于Cartan子代数的一些结果.
The authors studied some properties on n + 1 dimensional n - Lie algebras, and we proved that when dimension of dim A 1＞ 1, the dimension of Cartan subalgebra of A is n - 1. And also proved that n + k dimensional n - Lie algebra is simple if and only if it has not ideals that the dimension are not more than k and A = [ A A ], and other results about Cartan subalgebras of n - Lie algebras.
[1] 张知学, 李华君, 阎满富, ZHANG Zhi-xue, LI Hua-jun, YAN Man-fu. n-Lie代数的半单准则 [J]. 河北大学学报(自然科学版) 2001.doi:10.3969/j.issn.1000-1565.2001.01.002
[2] FILIPPPOV V T. n - Lie algebras [J]. Siberian Mathematical Journal 1985, 26(06).
[3] KASYNOV SH M. On a theory of n - Lie algebras [J]. Algebra and Logika 1990, 26(03).
[4] Bai RP., Li HJ., Shi HF., Zhang ZX.. The inner derivation algebras of (n+1) - dimensional n-Lie algebras [J]. Communications in algebra 2000, 6(6).
[5] KASYMOV Sh M. Conjugacy of Cartan subalgebras in n-Lie algebras [J]. Algebra I Logika 1995, 34(04).
[6] JAMES E Humohreys. Introduction to Lie algebras and representation theory [M]. New York: Springer-Verlag 1972.
