Results 41 to 50 of about 3,228 (247)
Automorphisms of Right-Angled Coxeter Groups
International Journal of Mathematics and Mathematical Sciences, 2008 If (𝑊,𝑆) is a right-angled Coxeter system, then Aut(𝑊) is a semidirect product of the group Aut∘(𝑊) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut∘(𝑊) is a semidirect product of Inn(𝑊)
Mauricio Gutierrez, Anton Kaul
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Incoherent Coxeter Groups [PDF]
Proceedings of the American Mathematical Society, 2016 We use probabilistic methods to prove that many Coxeter groups are incoherent. In particular, this holds for Coxeter groups of uniform exponent > 2
Jankiewicz, Kasia, Wise, Daniel T.
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The Tits alternative for non-spherical Pride groups [PDF]
, 2008 Pride groups, or 'groups given by presentations in which each defining relator involves at most two types of generators', include Coxeter groups, Artin groups, triangles of groups, and Vinberg's groups defined by periodic paired relations.
Williams, Gerald +5 more
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Proper affine actions for right-angled Coxeter groups [PDF]
Duke mathematical journal, 2018 For any right-angled Coxeter group $\Gamma$ on $k$ generators, we construct proper actions of $\Gamma$ on $\mathrm{O}(p,q+1)$ by right and left multiplication, and on the Lie algebra $\mathfrak{o}(p,q+1)$ by affine transformations, for some $p,q\in ...
J. Danciger +2 more
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Asymptotical behaviour of roots of infinite Coxeter groups I [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Let $W$ be an infinite Coxeter group, and $\Phi$ be the root system constructed from its geometric representation. We study the set $E$ of limit points of "normalized'' roots (representing the directions of the roots).
Christophe Hohlweg +2 more
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A word property for twisted involutions in Coxeter groups [PDF]
Electron. Notes Discret. Math., 2017 Given an involutive automorphism $\theta$ of a Coxeter system $(W,S)$, let $\mathfrak{I}(\theta) \subseteq W$ denote the set of twisted involutions. We provide a minimal set of moves that can be added to the braid moves, in order to connect all reduced $\
Mikael Hansson, Axel Hultman
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FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions
Sultan Qaboos University Journal for Science, 2014 We construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine extended Coxeter groups W(A3) and W(B3)=Aut(A3).
Nazife Özdeş Koca +2 more
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International Journal of Algebra and Computation, 2020 Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erdös–Rényi model). In this paper, we extend this model to study random general Coxeter groups and give some results about random Coxeter groups, including some information about the homology of the nerve of a ...
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Submaximal factorizations of a Coxeter element in complex reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 When $W$ is a finite reflection group, the noncrossing partition lattice $NC(W)$ of type $W$ is a very rich combinatorial object, extending the notion of noncrossing partitions of an $n$-gon.
Vivien Ripoll
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Determinantal hypersurfaces and representations of Coxeter groups [PDF]
Pacific Journal of Mathematics, 2018 Given a finite generating set $T=\{g_0,\dots, g_n\}$ of a group $G$, and a representation $\rho$ of $G$ on a Hilbert space $V$, we investigate how the geometry of the set $D(T,\rho)=\{ [x_0 : \dots : x_n] \in\mathbb C\mathbb P^n \mid \sum x_i\rho(g_i ...
Z. C̆uc̆ković +2 more
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