标题： 与光滑复代数簇的幂零基本群相关的幂零李代数的分次 显示英文标题

标题： Gradings on nilpotent Lie algebras associated with the nilpotent fundamental groups of smooth complex algebraic varieties

摘要： 设 $\Gamma$是一个单连通幂零李群 $N$中的格，其李代数 $\mathfrak{n}$是 $p$-滤子型。 我们证明当 $\Gamma$同构于光滑复代数簇的基本群时， $\Gamma$要么是交换的，要么是2步幂零的。 此外，作为我们结果的应用，我们给出了一个单连通幂零李群中维数小于或等于六的格同构于光滑复代数簇的基本群所需的条件。 显示英文摘要

摘要： Let $\Gamma$ be a lattice in a simply-connected nilpotent Lie group $N$ whose Lie algebra $\mathfrak{n}$ is $p$-filiform. We show that $\Gamma$ is either abelian or 2-step nilpotent if $\Gamma$ is isomorphic to the fundamental group of a smooth complex algebraic variety. Moreover as an application of our result, we give a required condition of a lattice in a simply-connected nilpotent Lie group of dimension less than or equal to six to be isomorphic to the fundamental group of a smooth complex algebraic variety.