Related papers: Artin HNN-extensions virtually embed in Artin grou…

The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincar\'e-Birkhoff-Witt theorem for involutive…

Recently, Cohen and Wales built a faithful linear representation of the Artin group of type $D_n$, hence showing the linearity of this group. It was later discovered that this representation is reducible for some complex values of its two…

An auxiliary free construction $*_{i=1}^{r}(K_i, L_i, t_i)_M$ based on HNN-extensions and on generalized free product of groups with amalgamated subgroups is suggested, and some of its basic properties are displayed. The proposed…

We develop a Hodge theory for relative simple normal crossing varieties over an Artinian base scheme. We introduce the notion of a mixed Hodge structure over an Artin ring, which axiomatizes the structure that is found on the cohomology of…

In Artin-Tits groups attached to Coxeter groups of spherical type, we give a combinatorial formula to express the simple elements of the dual braid monoids in the classical Artin generators. Every simple dual braid is obtained by lifting an…

For a fixed $n\ge2$, the Houghton group $H_n$ consists of bijections of $X_n=\{1,\ldots,n\} \times \mathbb{N}$ that are `eventually translations' of each copy of $\mathbb{N}$. The Houghton groups have been shown to have solvable conjugacy…

We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree…

We study Artin-Schelter Gorenstein fixed subrings of some Artin-Schelter regular algebras of dimension 2 and 3 under finite group actions, and prove a noncommutative version of the Kac-Watanabe and Gordeev theorem for these algebras.

Affine subgroups having the same Coxeter number with the affine Coxeter groups W(An), W(Dn), and W(En) are constructed by graph folding technique. The affine groups W(Cn) and W(Bn) are obtained from the Coxeter groups W(A2n-1) and W(D2n-1)…

The goal of this paper is to construct examples of centralizers in the Artin braid groups requiring the number of generators quadratic in the number of strings. These examples disprove a recent conjecture of N. Franco and J.…

We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G in Mod(S) satisfies certain conditions that imply G is…

We prove by explicit construction that graph braid groups and most surface groups can be embedded in a natural way in right-angled Artin groups, and we point out some consequences of these embedding results. We also show that every…

We study the right-angled Artin group action on the extension graph. We show that this action satisfies a certain finiteness property, which is a variation of a condition introduced by Delzant and Bowditch. As an application we show that…

We introduce the concept of hyperreflection groups, which are a generalization of Coxeter groups. We prove the Deletion and Exchange Conditions for hyperreflection groups, and we discuss special subgroups and fundamental sectors of…

In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…

We introduce the notion of metrically systolic simplicial complexes. We study geometric and large-scale properties of such complexes and of groups acting on them geometrically. We show that all two-dimensional Artin groups act geometrically…

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representatons of the corresponding Artin group A. The poset…

We study the class N of graphs, the right-angled Artin groups defined on which do not contain surface subgroups. We prove that a presumably smaller class N' is closed under amalgamating along complete subgraphs, and also under adding…

A result of Allock [1](arXiv:math/9907194) states that certain orbifold braid groups contain Artin groups of type $D_n$, $\tilde{B}_n$ and $\tilde{D}_n$ as finite index subgroups. The underlying orbifolds have at most two cone points of…