Automorphisms of Coxeter groups

2003/10/09 by Patrick Bahls, Bahls, Patrick · 2 citations
Mathematics · #20F28 (secondary) #20F55 (primary) #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F28 #msc:20F55

paper · pdf · doi:10.48550/arxiv.math/0310127

16 pages, no figures. Submitted to Trans. Amer. Math. Soc

arxiv created 2003/10/09 · openalex publication_date 2003/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute Aut(W) for any even Coxeter group whose Coxeter diagram is connected, contains no edges labeled 2, and cannot be separated into more than 2 connected components by removing a single vertex. The description is given explicitly in terms of the given presentation for the Coxeter group and admits an easy characterization of those groups W for which Out(W) is finite.

Cited by

• Profinite rigidity of crystallographic groups arising from Lie theory
• Rigidity of two-dimensional Coxeter groups

Related

• Coxeter quotients of the automorphism group of a Coxeter group
• The automorphism group of the universal Coxeter group
• Classification of Coxeter groups with finitely many elements of a-value 2
• Virtually splitting the map from Aut(G) to Out(G)
• Coxeter groups and automorphisms