Related papers: Sur les automorphismes et la rigidite des groupes …

A Coxeter system is an ordered pair (W,S) where S is the generating set in a particular type of presentation for the Coxeter group W. A subgroup of W is called special if it is generated by a subset of S. Amalgamated product decompositions…

We prove that every right-angled Artin group occurs as a finite-index subgroup of the outer automorphism group of another right-angled Artin group. We furthermore show that the latter group can be chosen in such a way that the quotient is…

A class of topological spaces is topologically rigid if any two spaces with the same fundamental group are also homeomorphic. Topological rigidity, in addition to its intrinsic interest, has been useful for solving abstract commensurability…

In this article, we discuss the notion of partition of elements in an arbitrary Coxeter system $(W,S)$: a partition of an element $w$ is a subset $\mathcal P\subseteq W$ such that the left inversion set of $w$ is the disjoint union of the…

Artin groups are a natural generalization of braid groups and are well-understood in certain cases. Artin groups are closely related to Coxeter groups. There is a faithful representation of a Coxeter group $W$ as a linear reflection group…

We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that a non-spherical and non-affine Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly)…

In this paper are described the groups of automorphisms of semigroup End(W(X)), where W(X) is free commutative or free associative algebra.

We show that right-angled Coxeter groups are relatively hyperbolic in the sense defined by Farb, relative to a natural collection of rank-2 parabolic subgroups.

Let W be a Coxeter group. In this paper, we establish that, up to going to some finite index normal subgroup W_0 of W, any two cyclically reduced expressions of conjugate elements of W_0 only differ by a sequence of braid relations and…

By the work of Sela, for any free group $F$, the Coxeter group $W_ 3 = \mathbb{Z}/2\mathbb{Z} \ast \mathbb{Z}/2\mathbb{Z} \ast \mathbb{Z}/2\mathbb{Z}$ is elementarily equivalent to $W_3 \ast F$, and so Coxeter groups are not closed under…

The automorphism groups ${\rm Aut\,}A_n$ and ${\rm Aut\,}W_n$ of the polynomial algebra $A_n=C[x_1,x_2,\cdots, x_n]$ and the rank $n$ Witt algebra $W_n={\rm Der\,}A_n$ are studied in this paper. It is well-known that ${\rm Aut\,}A_n$ for…

Given a field $K$, we investigate which subgroups of the group Aut$\mathbb{A}^2_K$ of polynomial automorphisms of the plane are linear or not. The results are contrasted. The group Aut$\mathbb{A}^2_K$ itself is nonlinear, except if $K$ is…

Given a Coxeter system (W,S) equipped with an involutive automorphism T, the set of twisted identities is i(T) = {T(w)^{-1}w : w \in W}. We point out how i(T) shows up in several contexts and prove that if there is no s \in S such that…

Let W be an irreducible, finitely generated Coxeter group. The geometric representation provides an discrete embedding in the orthogonal group of the so-called Tits form. One can look at the representation modulo the kernel of this form; we…

If $(W,S)$ is a right-angled Coxeter system and $W$ has no $\mathbb Z^3$ subgroups, then it is shown that the absence of an elementary separation property in the presentation diagram for $(W,S)$ implies all CAT(0) spaces acted on…

We study the automorphisms of graph products of cyclic groups, a class of groups that includes all right-angled Coxeter and right-angled Artin groups. We show that the group of automorphism generated by partial conjugations is itself a…

In this paper we investigate the endomorphism algebras of standard cluster tilting objects in the stably 2-Calabi-Yau categories $\Sub{\Lambda_w}$ with elements $w$ in Coxeter groups in \cite{BIRSc}. They are examples of the 2-Auslander…

The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…

Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erd\"os-R\'enyi model). In this paper, we extend this model to study random general Coxeter groups…

We construct a family of right-angled Coxeter groups which provide counter-examples to questions about the stable boundary of a group, one-endedness of quasi-geodesically stable subgroups, and the commensurability types of right-angled…