Results 61 to 70 of about 285 (147)

A strong characterization of the entries of the Burau matrices of $4$-braids: The Burau representation of the braid group $B_4$ is faithful almost everywhere

open access: yes, 2022
We establish strong constraints on the kernel of the (reduced) Burau representation $\beta_4:B_4\to \text{GL}_3\left(\mathbb{Z}\left[q^{\pm 1}\right]\right)$ of the braid group $B_4$.
Datta, Amitesh
core  

Schur–Weyl-Type Duality for Quantized gl(1|1), the Burau Representation of Braid Groups, and Invariants of Tangled Graphs

open access: yes, 2011
We show that the Schur-Weyl-type duality between g(1|1) and GL n gives a natural representation-theoretic setting for the relationship between reduced and introduced Burau representations.
Reshetikhin, N.   +5 more
core   +1 more source

Extensions of Tong-Yang-Ma representation

open access: yes, 2020
International audienceIn 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
Takano, Akihiro, Soulié, Arthur
core   +1 more source

Characterizing the kernel of the Burau representation modulo 2 for the 4-strand braid group

open access: yes, 2023
In 1997, Cooper-Long established the nontriviality of the kernel of the modulo 2 Burau representation for the 4-strand braid group, $B_4$. This paper extends their work by embedding the image group into a finitely presented group.
Lee, Donsung
core  

Topological braiding and virtual particles on the cell membrane. [PDF]

open access: yesProc Natl Acad Sci U S A, 2021
Liu J   +6 more
europepmc   +1 more source

On the considerations adopted by Breidze and Traczyk towards the faithfulness of Burau representation for $n=4$

open access: yes, 2022
This work discusses the open problem of the faithfulness of the reduced Burau representation for $n=4$. Birman showed that in order to prove this representation is faithful, it is sufficient to find two matrices $A$ and $B$ that generate a free group of ...
Abdulrahim, Mohammad N.   +1 more
core  

Biochar-based fertilizers and their applications in plant growth promotion and protection. [PDF]

open access: yes3 Biotech, 2022
Agarwal H   +5 more
europepmc   +1 more source

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