Results 61 to 70 of about 51,088 (236)
Intersection of parabolic subgroups in Euclidean braid groups: a short proof
Comptes Rendus. MathématiqueWe give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A[\tilde{A}_n]$ is again a parabolic subgroup. To that end, we use that the spherical-type Artin group
Cumplido, María +2 more
doaj +1 more source
Pure braid groups are not residually free
, 2011 We show that the Artin pure braid group on at least four strands is not residually free.
Cohen, Daniel C. +2 more
core +1 more source
The shift‐homological spectrum and parametrising kernels of rank functions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift‐homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical.
Isaac Bird +2 more
wiley +1 more source
Locally Non-spherical Artin Groups
Journal of Algebra, 1998 Let \(S\) be a finite nonempty set, and let \(M=(m_{a,b})_{a,b\in S}\) be a Coxeter matrix over \(S\). For \(m\) in \(\mathbb{N}\cup\{\infty\}\) and \(a,b\) in \(S\), let \(w(a,b;m)\) denote \((ab)^{{m\over 2}}\) if \(m\) is even, \((ab)^{{m-1\over 2}}a\) if \(m\) is odd, and \(1\) if \(m\) is \(\infty\).
openaire +1 more source
Embedability between right-angled Artin groups [PDF]
Geometry & Topology, 2013 In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph $\gam$, we produce a new graph through a purely combinatorial procedure, and call it the extension graph $\gam^e$ of $\gam$. We produce a second graph $\gam^e_k$, the clique graph of $\gam^e$, by adding extra vertices for each complete ...
Kim, SH Kim, Sang-hyun +1 more
openaire +4 more sources
The m$m$‐step solvable anabelian geometry of mixed‐characteristic local fields
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract Let K$K$ be a mixed‐characteristic local field. For an integer m⩾0$m \geqslant 0$, we denote by Km/K$K^m / K$ the maximal m$m$‐step solvable extension of K$K$, and by GKm$G_K^m$ the maximal m$m$‐step solvable quotient of the absolute Galois group GK$G_K$ of K$K$.
Seung‐Hyeon Hyeon
wiley +1 more source
Parabolic Subgroups of Artin Groups
Journal of Algebra, 1997 Let \((A,\Sigma)\) be an Artin system. For \(X\subseteq\Sigma\) by \(A_X\) is denoted the subgroup of \(A\) generated by \(X\). Such a group is called a parabolic subgroup of \(A\). Van der Lek's theorem is reproved: ``A parabolic subgroup of an Artin group is an Artin group''.
openaire +1 more source
Anti-trees and right-angled Artin subgroups of braid groups
, 2015 We prove that an arbitrary right-angled Artin group $G$ admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree.
Kim, Sang-hyun, Koberda, Thomas
core +1 more source
GL‐algebras in positive characteristic II: The polynomial ring
Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.Abstract We study GL$\mathbf {GL}$‐equivariant modules over the infinite variable polynomial ring S=k[x1,x2,…,xn,…]$S = k[x_1, x_2, \ldots, x_n, \ldots]$ with k$k$ an infinite field of characteristic p>0$p > 0$. We extend many of Sam–Snowden's far‐reaching results from characteristic zero to this setting.
Karthik Ganapathy
wiley +1 more source
On Certain 3-Generator Artin Groups [PDF]
Transactions of the American Mathematical Society, 1987 The author considers three infinite 3-generator Artin groups \[ S= \] \[ T= \] \[ U=. \] Their Coxeter diagrams are the smallest for which the groups are infinite. The main result is that S, T, and U are semidirect products of a free group of countable, infinite rank with an appropriate 2-generator Artin group.
openaire +2 more sources