发表机构
Ben-Gurion University of the Negev（内盖夫本-古里安大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究自由profinite群的下p-中心滤过与第二上同调群之间的对偶，证明由Lyndon词索引的自然基在配对下几乎完全对偶，且配对值不依赖于滤过层级。
AI 中文摘要
设$S$是有限有序基$X$上的自由profinite群，并设$S^{(n,p)}$（$n=1,2,\ldots$）表示其下$p$-中心滤过。$S^{(n,p)}/S^{(n+1,p)}$与$H^2(S/S^{(n,p)},\mathbb{F}_p)$之间存在自然对偶。这些$\mathbb{F}_p$-线性空间具有由字母表$X$中长度不超过$n$的Lyndon词索引的自然基。已知这些基是单位三角对偶的。我们证明它们更接近于完全对偶，通过表明两个基元素之间的配对除非对应的Lyndon词互为排列，否则为零。我们进一步表明，配对的值本质上与$n$无关。
英文摘要
Let $S$ be a free profinite group on a finite ordered basis $X$, and let $S^{(n,p)}$, $n=1,2,\ldots,$ denote its lower $p$-central filtration. There is a natural duality between $S^{(n,p)}/S^{(n+1,p)}$ and $H^2(S/S^{(n,p)},\mathbb{F}_p)$. These $\mathbb{F}_p$-linear spaces admit natural bases indexed by Lyndon words of length $\leq n$ in the alphabet $X$. These bases are known to be unitriangularly dual. We prove that they are much closer to being fully dual, by showing that the pairing between two basis elements vanishes unless the corresponding Lyndon words are permutations of one another. We further show that the value of the pairing is essentially independent of $n$.
