Locally finite continuations and Coxeter groups of infinite ranks

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Muehlherr, Bernhard¹  Nuida, Koji^2,3 

[1] Justus Liebig Univ Giessen, Math Inst, Giessen, Germany

[2] Univ Tokyo, Grad Sch Informat Sci & Technol, Tokyo, Japan

[3] Natl Inst Adv Ind Sci & Technol, Cyber Phys Secur Res Ctr, Tokyo, Japan

关键词: Coxeter groups;    Isomorphism problem;    Intrinsic reflections;   

DOI  :  10.1016/j.jpaa.2020.106464

来源: Elsevier

【 摘 要 】

An involution r in a Coxeter group W is called an intrinsic reflection of W if r is an element of S-W for each Coxeter generating set S of W. In recent joint work with R.B. Howlett [13] we determined all intrinsic reflections in finitely generated Coxeter groups. In the present paper we extend this result to the infinite rank case. An important tool in [13] is the notion of the finite continuation of an involution that is only meaningful for finitely generated Coxeter groups. Here we introduce the locally finite continuation for any subset of an arbitrary group which enables us to deal with Coxeter groups of infinite rank. We apply our result to show that certain classes of Coxeter groups are reflection independent and we investigate rigidity of 2-spherical Coxeter systems of arbitrary ranks. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free