Locally finite continuations and Coxeter groups of infinite ranks

Bernhard Mühlherr, Koji Nuida

研究成果: Contribution to journalArticle査読

抄録

An involution r in a Coxeter group W is called an intrinsic reflection of W if r∈SW 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.

本文言語英語
論文番号106464
ジャーナルJournal of Pure and Applied Algebra
225
1
DOI
出版ステータス出版済み - 1 2021
外部発表はい

All Science Journal Classification (ASJC) codes

  • 代数と数論

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