n-李代数的Hypo-幂零理想

Hypo-Nilpotent ideals of n-Lie algebras

研究n-李代数的Hypo-幂零理想,及具有5维极大Hypo-幂零理想的所有可解3-李代数的结构。证明可解非幂零n-李代数一定存在Hypo-幂零理想,且其幂零根基的余维数等于1。给出可解非幂零3-李代数的极大Hypo-幂零理想与3-李代数的维数关系。对具有一类特殊5-维极大次幂零理想的可解3-李代数的每一类3-李代数,分别研究了其导代数维数序列DS及下降中心维数序列CS,及他们之间的关系。

The Hypo-nilpotent ideals of n-Lie algebras and the algebraic structure of solvable 3-Lie algebras which have a 5 dimensional Hypo-nilpotent ideal N are mainly concerned. It is proven that there exist Hypo-nilpotent ideals for the solvable non-nilpotent n-Lie algebras, and the co-dimension of the nilpotent radical is one. The dimensional relations between the maximal Hypo-nilpotent ideals of solvable non-nilpotent 3-Lie algebras and 3-Lie algebras are offered. For a class of 3-Lie algebras which have special a 5 dimensional nilpotent ideal, the dimension sequence DS of derivative algebras and the decreased center the dimension sequence CS and their relations are considered.