Automorphisms of Coxeter Groups of Rank 3 with Infinite Bonds
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TLDR
In this paper, the automorphism group of a rank 3 Coxeter group with at least one infinite bond in the Coxeter diagram is described, and the automomorphism group is shown to be larger than the group generated by the inner automorphisms.About:
This article is published in Journal of Algebra.The article was published on 2002-02-01 and is currently open access. It has received 10 citations till now. The article focuses on the topics: Coxeter complex & Coxeter element.read more
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Journal ArticleDOI
Automorphisms of nearly finite Coxeter groups.
W.N. Franzsen,R.B. Howlett +1 more
TL;DR: In this article, it was shown that the Coxeter diagram of W has no edges with infinite labels and that any automorphism of W that preserves reflections lies in the subgroup of AutðW Þ generated by the inner automorphisms and the automomorphisms induced by symmetries of WJ of rank n � 1.
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Automorphisms of Coxeter groups
TL;DR: In this article, the authors give a characterization of even Coxeter groups 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.
Journal ArticleDOI
Automorphisms of Coxeter groups
TL;DR: In this article, the authors give a characterization of even Coxeter groups 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.
Journal ArticleDOI
Bowditch’s Q-conditions and Minsky’s primitive stability
Jaejeong Lee,Binbin Xu +1 more
TL;DR: For the action of the outer automorphism group of the rank two free group on the corresponding variety of PSL(2,C) characters, two domains of discontinuity have been known to exist that are strictly larger than the set of Schottky characters as mentioned in this paper.
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Centralizers of reflections and reflection-independence of Coxeter groups
TL;DR: In this paper, a Coxeter group W is called reflection independent if its reflections are uniquely determined by W only, independently on the choice of the generating set, and a new sufficient condition for the reflection independence is given, and examined for Coxeter groups in certain classes, possibly of infinite ranks.
References
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Book
Groupes et algèbres de Lie
TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
Book
Finite Groups of Lie Type: Conjugacy Classes and Complex Characters
TL;DR: The Steinberg Character as discussed by the authors is a character of Deligne-Lusztig, which is a generalization of the Steinberg character of Cuspidal Representations.
Journal ArticleDOI
Reflection subgroups of Coxeter systems
TL;DR: In this article it was shown that a Coxeter group is a reflection subgroup of the root system of a reflection system, and that a set of reflections can be the set of canonical generators of such a group in terms of the inner products of the cocycle.