A finiteness property and an automatic structure for Coxeter groups
type: Item
instance of: scholarly article
title: A finiteness property and an automatic structure for Coxeter groups
zbMATH Open document ID: 0793.20036
DOI: 10.1007/BF01445101
author: Brigitte Brink
author: R. B. Howlett
published in: Mathematische Annalen
publication date: 1994-08-14T00:00:00Z
full work available at URL: https://eudml.org/doc/165081
review text: If \(\alpha\) and \(\beta\) are positive roots in the root system of a Coxeter group \(W\), we say that \(\alpha\) dominates \(\beta\) if \(w\cdot\beta\) is negative for every \(w\in W\) such that \(w\cdot\alpha\) is negative. It is shown that if the distinguished generating set of \(W\) is finite, then the set of all positive roots \(\alpha\) for which there is no \(\beta\) dominated by \(\alpha\) is finite. It follows as a consequence that the group \(W\) is automatic.
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 68Q45
Mathematics Subject Classification ID: 68Q70
zbMATH DE Number: 537293
zbMATH Keywords: Coxeter groups
zbMATH Keywords: automatic groups
zbMATH Keywords: positive roots
zbMATH Keywords: root systems
zbMATH Keywords: generating sets
Wikidata QID: Q56213652
MaRDI profile type: Publication
cites work: Q5580319
cites work: Coxeter groups are almost convex
cites work: Small cancellation theory and automatic groups
cites work: Schubert calculus of a Coxeter group
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description: scientific article; zbMATH DE number 537293