Rigidity of Coxeter groups and Artin groups

被引:43
|
作者
Brady, N
McCammond, JP
Mühlherr, B
Neumann, WD
机构
[1] Univ Oklahoma, Dept Math, Norman, OK 73019 USA
[2] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
[3] Univ Dortmund, Fachbereich Math, D-44221 Dortmund, Germany
[4] Columbia Univ Barnard Coll, Dept Math, New York, NY 10027 USA
基金
美国国家科学基金会;
关键词
Coxeter groups; Artin groups; diagram twisting; rigidity;
D O I
10.1023/A:1020948811381
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A Coxeter group is rigid if it cannot be defined by two nonisomorphic diagrams. There have been a number of recent results showing that various classes of Coxeter groups are rigid, and a particularly interesting example of a nonrigid Coxeter group has been given by Bernhard Muhlherr. We show that this example belongs to a general operation of 'diagram twisting'. We show that the Coxeter groups defined by twisted diagrams are isomorphic, and, moreover, that the Artin groups they define are also isomorphic, thus answering a question posed by Charney. Finally, we show a number of Coxeter groups are reflection rigid once twisting is taken into account.
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页码:91 / 109
页数:19
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