Bipolar Coxeter groups

JOURNAL OF ALGEBRA

卷:338

Article

Caprace, Pierre-Emmanuel²  Przytycki, Piotr¹ 

[1] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

[2] Catholic Univ Louvain, Dept Math, B-1348 Louvain, Belgium

关键词: Coxeter groups;    Isomorphism problem;   

DOI  :  10.1016/j.jalgebra.2011.05.007

来源: Elsevier

【 摘 要 】

We consider the class of those Coxeter groups for which removing from the Cayley graph any tubular neighbourhood of any wall leaves exactly two connected components. We call these Coxeter groups bipolar. They include the virtually Poincare duality Coxeter groups, the pseudo-manifold Coxeter groups and the infinite irreducible 2-spherical ones. We show in a geometric way that a bipolar Coxeter group admits a unique conjugacy class of Coxeter generating sets. Moreover, we provide a characterisation of bipolar Coxeter groups in terms of the associated Coxeter diagram. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free