A decomposition theorem for higher rank Coxeter groups

2010/07/21 by Ryan Blair, Blair, Ryan, Ryan Ottman +1
Computer Science · Mathematics · #20F55 #51F15 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20F55 #msc:51F15 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1007.3755

7 pages, 3 figures

arxiv created 2010/07/21 · openalex publication_date 2010/07/21 · arxiv updated 2010/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that any Coxeter graph which defines a higher rank Coxeter group must have disjoint induced subgraphs each of which defines a hyperbolic or higher rank Coxeter group. We then use this result to demonstrate several classes of Coxeter graphs which define hyperbolic Coxeter groups.

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