论文标题
Coxeter组的星系
The galaxy of Coxeter groups
论文作者
论文摘要
在本文中，我们介绍了Coxeter组的星系 - 无限的尺寸，局部有限的，排名的简单复合物，可捕获Coxeter系统之间的同构。通过这样做，我们想提出一个新的框架，以研究Coxeter组的同构问题。我们证明了有关此空间的一些结构性结果，提供了小等级的完整表征，并提出了许多问题。此外，我们调查已知工具，结果和猜想。在此过程中，我们显示了三角形Coxeter群体的刚性刚度 - 这可能是独立的。
In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to study the isomorphism problem for Coxeter groups. We prove some structural results about this space, provide a full characterization in small ranks and propose many questions. In addition we survey known tools, results and conjectures. Along the way we show profinite rigidity of triangle Coxeter groups -- a result which is possibly of independent interest.
