相关论文: Cabling Burau Representation

For any n>3, we give a family of finite dimensional irreducible representations of the braid group B_n. Moreover, we give a subfamily parametrized by 0<m<n of dimension the combinatoric number (n,m). The representation obtained in the case…

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…

We prove that there are no irreducible representations of $B_n$ of dimension $n+1$ for $n\geq 10.$

In [1] we have constructed a [n+1/2]+1 parameters family of irreducible representations of the Braid group B_3 in arbitrary dimension using a $q-$deformation of the Pascal triangle. This construction extends in particular results by S.P.…

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 that the image of the Full braid group $B_{n+1}$ on $n+1$ strands under the Burau representation, evaluated at a primitive $d$-th root of unity is arithmetic provided $n\geq d$.

We linearize the Artin representation of the braid group given by (right) automorphisms of a free group providing a linear faithful representation of the braid group. This result is generalized to obtain linear representations for the…

We use a geometric approach to show that the reduced Burau representation specialized at roots of unity has another incarnation as the monodromy representation of a moduli space of Euclidean cone metrics on the sphere, as described by…

This article gives certain fibre bundles associated to the braid groups which are obtained from a translation as well as conjugation on the complex plane. The local coefficient systems on the level of homology for these bundles are given in…

This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…

A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their…

For $n\geq 2$, let $G_n$ be a group and let $\rho: B_n\rightarrow G_n$ be a representation of the braid group $B_n$. For a field $\mathbb{K}$ and $a,b,c\in \mathbb{K}$, Bardakov, Chbili, and Kozlovskaya extend the representation $\rho$ to a…

We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…

This classification is found by analyzing the action of a normal subgroup of $B_3$ as hyperbolic isometries. This paper gives an example of an unfaithful specialization of the Burau representation on $B_4$ that is faithful when restricted…

In a recent paper by L. A. Bokut, V. V. Chaynikov and K. P. Shum in 2007, Braid group $B_n$ is represented by Artin-Burau's relations. For such a representation, it is told that all other compositions can be checked in the same way. In this…

In 1996, Tong, Yang and Ma defined a family of representations of the braid group which have the same dimensions as the (unreduced) Burau representations but are not equivalent. The Burau representation was defined homologically and…

In the present paper we study structural aspects of certain quotients of braid groups and virtual braid groups. In particular, we construct and study linear representations $B_n\to {\rm GL}_{n(n-1)/2}\left(\mathbb{Z}[t^{\pm1}]\right)$,…

We study the representations of the commutator subgroup of the braid group with n strands in the symmetric group of degree r. Motivated by some experimental results, we conjecture that for n>r, every such representation is trivial.

Braiding is a geometric concept that manifests itself in a variety of scientific contexts from biology to physics, and has been employed to classify bulk band topology in topological materials. Topological edge states can also form braiding…

Consider the kernel Mag_g of the Magnus representation of the Torelli group and the kernel Bur_n of the Burau representation of the braid group. We prove that for g >= 2 and for n >= 6 the groups Mag_g and Bur_n have infinite rank first…