Related papers: Infinitary braid groups
Virtual knots arise in the study of Gauss diagrams and Vassiliev invariants of usual knots. Virtual braids correspond naturally to virtual knots. We consider the group of virtual braids on n strings VB_n and its Burau representation, in…
A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…
The paper deals with braided Clifford algebras, understood as Chevalley-Kahler deformations of braided exterior algebras. It is shown that Clifford algebras based on involutive braids can be naturally endowed with a braided quantum group…
We consider a conformal invariant of braids, the extremal length with totally real horizontal boundary values $\lambda_{tr}$. The invariant descends to an invariant of elements of $\mathcal{B}_n\diagup\mathcal{Z}_n$, the braid group modulo…
We give another proof for a result of Brick stating that the simple connectivity at infinity is a geometric property of finitely presented groups. This allows us to define the rate of vanishing of $\p1i$ for those groups which are simply…
Let G be a chordal graph, X(G) the complement of the associated complex arrangement and Gamma(G) the fundamental group of X(G). We show that Gamma(G) is a limit of colored braid groups over the poset of simplices of G. When G = G_T is the…
The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…
A new presentation of the $n$-string braid group $B_n$ is studied. Using it, a new solution to the word problem in $B_n$ is obtained which retains most of the desirable features of the Garside-Thurston solution, and at the same time makes…
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
It is known that the pure braid groups are residually torsion-free nilpotent. This property is however widely open for the most obvious generalizations of these groups, like pure Artin groups and like fundamental groups of hyperplane…
We develop a new approach to the linear ordering of the braid group $B\_n$, based on investigating its restriction to the set $\Div(\Delta\_n^d)$ of all divisors of $\Delta\_n^d$ in the monoid $B\_\infty^+$, i.e., to positive $n$-braids…
Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial…
We determine the image of the braid groups inside the Temperley-Lieb algebras, defined over finite field, in the semisimple case, and for suitably large (but controlable) order of the defining (quantum) parameter. We also prove that, under…
In this article, we study the irreducibility of representations of the singular braid group on $n$ strands, namely $SB_n$. Our first finding is the determination of the forms of all irreducible representations $\rho : SB_2 \to…
We prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. This leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type $F_n$ but not…
We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are…
A group has finite palindromic width if there exists $n$ such that every element can be expressed as a product of $n$ or fewer palindromic words. We show that if $G$ has finite palindromic width with respect to some generating set, then so…
We determine the image of the braid groups inside the Iwahori-Hecke algebras of type A, when defined over a finite field, in the semisimple case, and for suitably large (but controlable) order of the defining (quantum) parameter.
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…
We give criteria on an inverse system of finite groups that ensure the limit is just infinite or hereditarily just infinite. More significantly, these criteria are 'universal' in that all (hereditarily) just infinite profinite groups arise…