报告时间：2019年10月11日（周五）下午16:00-17:00
报告地点：维格堂417
报告摘要：By Levi's theorem and complete classification of semisimple Lie algebras, the classification of solvable Lie algebras is thus an essential step in the classification of all finite-dimensional Lie algebras over fields of characteristic zero. But it seems to be neither feasible nor fruitful to proceed by dimension in the classification of solvable Lie algebra $\frak g$ beyond $\dim{\frak g}=6$. It is however possible to proceed by structure. An ideal $\frak n$ of the Lie algebra $\frak L$ is called a near perfect ideal if $[\frak L, \frak n]=\frak n$. The largest near perfect ideal of $\frak L$ exists, which is called the near perfect radical of $\frak L$ and denoted by $NP(\frak L)$. One important conclusion is that the factor algebra $\frak L/NP(\frak L)$ is nilpotent. For a solvable Lie algebra $\frak g$, its near perfect radical $NP(\frak g)$ is also nilpotent. So the factor algebra $\frak g/NP(\frak g)$ is called the left nilpotent algebra of $\frak g$, and $NP(\frak g)$ is called the right nilpotent algebra of $\frak g$, and denote them as $LN(\frak g)$ and $RN(\frak g)$ respectively. Here, we consider the left nilpotent algebra $LN(\frak g)$ is a $m$-dimensional abelian Lie algebra $A(m)$ and the right nilpotent algebra $RN(\frak g)$ is an $n$-dimensional model filiform Lie algebra ${\frak N}_n$.
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