论文标题
部分可观测时空混沌系统的无模型预测
The Image of the Gassner Representation of the Pure Braid Subgroup has Pairwise Free Generators
论文作者
论文摘要
尽管对Burau代表的忠诚知之甚少，但对于每$ n \ geq 4 $的每$ b_n $来说，Gassner代表的问题仍然开放。我们首先找到了Ainshel，Ainshel，Goldfeld和Lemieux的彩色布劳表示的定义，我们表明，这是等于Gassner代表的纯编织子组。 Abdulrahim和Knudson的方法需要在纯编织组的自由亚组的下中央系列中进行分析。但是，Lipschutz的工作提供了一种分析Gassner表示形式的方法，而彩色布劳结构将这种分析降低到基本的线性代数。
While much is known about the faithfulness of the Burau representation, the problem remains open for the Gassner representation for every $B_n$ with $n\geq 4$. We first find the definition of the Colored-Burau representation of Ainshel, Ainshel, Goldfeld, and Lemieux and we show that this is equivalent, when restricted to the pure braid subgroup, to the Gassner representation. The methods of Abdulrahim and Knudson require analysis within the lower central series of a free subgroup of the pure braid group. However, Lipschutz's work gives a method for analyzing the Gassner representation and the Colored-Burau structure reduces this analysis to basic linear algebra.
