论文标题
Nilpotent Quandles
Nilpotent quandles
论文作者
论文摘要
一个尼尔疗法的困境是一个群体，其内形群是nilpotent的。在以前的作品中，这种难题被称为还原性，但事实证明，他们的行为实际上非常接近群体的努力。特别是，我们表明，很容易表征生成此类难题的集合，并且它们具有HOPF属性。我们还展示了如何从免费的nilpotent群体中构建免费的nilpotent Quandles。然后，我们使用Nilpotent Quandles的属性来描述其相关组的简单呈现，并使用它来恢复Lebed和Mortier [LM21]对Abelian Quandles的分类。我们还研究了减少的问题，我们表明，减少的基本问题是等效的，作为链接的不变性，与降低的外围系统相同，从而增强了Hughes [Hug11]的先前结果。最后，我们从辫子的相关不变式角度给出了尼尔兽的特征。
A nilpotent quandle is a quandle whose inner automorphism group is nilpotent. Such quandles have been called reductive in previous works, but it turns out that their behaviour is in fact very close to nilpotency for groups. In particular, we show that it is easy to characterise generating sets of such quandles, and that they have the Hopf property. We also show how to construct free nilpotent quandles from free nilpotent groups. We then use the properties of nilpotent quandles to describe a simple presentation of their associated group, and we use this to recover the classification of abelian quandles by Lebed and Mortier [LM21]. We also study reduced quandles, and we show that the reduced fundamental quandle is equivalent, as an invariant of links, to the reduced peripheral system, sharpening a previous result of Hughes [Hug11]. Finally, we give a characterisation of nilpotency in terms of the associated invariants of braids.
