Reflection groups of geodesic spaces and Coxeter groups

被引：5
|
作者：
Hosaka, Tetsuya [1 ]
机构：
[1] Utsunomiya Univ, Dept Math, Utsunomiya, Tochigi 3218505, Japan
来源：
TOPOLOGY AND ITS APPLICATIONS | 2006年 / 153卷 / 11期
关键词：
reflection groups; Coxeter groups;
D O I：
10.1016/j.topol.2005.06.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
H.S.M. Coxeter showed that a group Gamma is a finite reflection group of an Euclidean space if and only if Gamma is a finite Coxeter group. In this paper, we define reflections of geodesic spaces in general, and we prove that Gamma is a cocompact discrete reflection group of some geodesic space if and only if Gamma is a Coxeter group. (C) 2005 Elsevier B.V. All rights reserved.
引用
收藏
页码：1860 / 1866
页数：7
相关论文
共 50 条
  • [21] Decompositions of groups by direct product and Coxeter groups
    de Cornulier, Yves
    de la Harpe, Pierre
    GEOMETRIC GROUP THEORY, 2007, : 75 - +
  • [22] On reflection representations of Coxeter groups over non-commutative rings
    Pilkington, Annette
    COMMUNICATIONS IN ALGEBRA, 2023, 51 (11) : 4567 - 4596
  • [23] Interval groups related to finite Coxeter groups I
    Baumeister, Barbara
    Neaime, Georges
    Rees, Sarah
    ALGEBRAIC COMBINATORICS, 2023, 6 (02): : 471 - 506
  • [24] Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
    Douvropoulos, Theo
    Lewis, Joel Brewster
    Morales, Alejandro H.
    JOURNAL OF ALGEBRA, 2024, 641 : 648 - 715
  • [25] A COMBINATORIAL CHARACTERIZATION OF COXETER GROUPS
    Marietti, Mario
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2009, 23 (01) : 319 - 332
  • [26] Depth in classical Coxeter groups
    Eli Bagno
    Riccardo Biagioli
    Mordechai Novick
    Alexander Woo
    Journal of Algebraic Combinatorics, 2016, 44 : 645 - 676
  • [27] On isomorphisms between Coxeter groups
    Mühlherr, B
    DESIGNS CODES AND CRYPTOGRAPHY, 2000, 21 (1-3) : 189 - 189
  • [28] Sylvester waves in the Coxeter groups
    Fel, LG
    Rubinstein, BY
    RAMANUJAN JOURNAL, 2002, 6 (03) : 307 - 329
  • [29] Sylvester Waves in the Coxeter Groups
    Leonid G. Fel
    Boris Y. Rubinstein
    The Ramanujan Journal, 2002, 6 : 307 - 329
  • [30] On Growth Functions of Coxeter Groups
    Bischof, Sebastian
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2025,
12345