M. Abdulrahim

activity

20162023

collaborators

7 papers

math.GR2023

Irreducible representations of the braid group $B_{3}$ in dimension 6

Taher I. Mayassi, Mohammad N. Abdulrahim

We use $q$ -Pascal's triangle to define a family of representations of dimension 6 of the braid group $B_{3}$ on three strings. Then we give a necessary and sufficient condition for t…

math.GR2022

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

Rawia A. Jinani, Mohammad N. Abdulrahim

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…

math.RT2021

On The Faithfulness of the extension of Lawrence-Krammer representation of the group of conjugating automorphisms C_3

Mohamad N. Nasser, Mohammad N. Abdulrahim

Let $C_{n}$ be the group of conjugating automorphisms. We study the representation $ρ$ of $C_{n}$ , an extension of Lawrence-Krammer representation of the braid group $B_{n}$ , defined by…

math.GR2020

Representations of the necklace braid group {NB}}_n of dimension (n=2,3,4)

Taher I. Mayassi, Mohammad N. Abdulrahim

We consider the irreducible representations each of dimension 2 of the necklace braid group $N B_{n}$ ( $n = 2, 3, 4$ ). We then consider the tensor product of the representations…

math.GR2020

On the irreducibility of the extensions of Burau and Gassner representations

Mohamad N. Nasser, Mohammad N. Abdulrahim

We study the $n$ th degree representations $ρ_{G}^$ of $C b_{n}$ and $ρ_{B}^$ of $C_{n}$ , defined by Valerij G. Bardakov, where $C b_{n}$ is the group of basis conjugating autom…

math.RT2019

Irreducibility of the three dimensional Albeverio-Rabanovich representation of the pure braid group $P_{3}$

Hasan A. Haidar, Mohammad N. Abdulrahim

We consider Albeverio- Rabanovich linear representation $π$ of the braid group $B_{3}$ . After specializing the indeterminates used in defining the representation to non-zero complex…

math.GR2016

On the Irreducibility of the Complex Specialization of the Representation of The Hecke Algebra of the Complex Reflection Group $G_{7}$

Mohammad Y. Chreif, Mohammad N. Abdulrahim

We consider a 2-dimensional representation of the Hecke algebra $H (G_{7}, u)$ , where $G_{7}$ is the complex reflection group and $u$ is the set of indeterminates $u=(x_1, x_2…

Irreducible representations of the braid group B3​ in dimension 6

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