论文标题
通过最长元素的纯编织组演示
Pure Braid Group Presentations via Longest Elements
论文作者
论文摘要
本文给出了古典纯编织组的新简化介绍。发电机是由连接子图的最长元素的平方给出的，我们证明唯一的关系是换向器，或者是某些Palindromic长度5箱关系。该介绍是由代数几何形状中的Twist函子激励的，但证明完全是Coxeter理论。我们还证明，类似集并非为所有Coxeter排列产生，这特别回答了Donovan和Wemyss的问题。
This paper gives a new, simplified presentation of the classical pure braid group. The generators are given by the squares of the longest elements over connected subgraphs, and we prove that the only relations are either commutators or certain palindromic length 5 box relations. This presentation is motivated by twist functors in algebraic geometry, but the proof is entirely Coxeter-theoretic. We also prove that the analogous set does not generate for all Coxeter arrangements, which in particular answers a question of Donovan and Wemyss.
