M. N. Nasser

activity

20202026

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18 papers · 1 filter

math.RT2026

On the structure of the singular triplet monoid and its virtual extension

Carmen Caprau, Mohamad N. Nasser

In this article, we introduce two new algebraic structures associated with the triplet group on $n$ strands, $L_{n}$ : the singular triplet monoid $S L M_{n}$ and its virtual extension $V…

math.RT2026

Multi-welded twin groups

Mohamad N. Nasser, Oscar Ocampo

For $k \geq 1$ and $n \geq 2$ , we introduce the multi-welded twin group $M_{k} W T_{n}$ , a natural welded analogue of the multi-virtual twin group. We show that $M_{k} W T_{n}$ arises naturally…

math.RT2026

On Universal Virtual and Welded Braid Groups and Their Linear Representations

Mohamad N. Nasser, Oscar Ocampo

We introduce linear representations of the universal virtual braid group $U V_{n} (c)$ , where $n \geq 2$ and $c \geq 1$ , which is a unifying framework for braid-type groups with multiple…

math.RT2026

On representations of the triplet group and some of its extensions

Mohamad N. Nasser, Nafaa Chbili, Khaled Qazaqzeh

In this paper, we study the representations of the triplet group $L_{n}$ , where $n$ is a positive integer, together with their extensions to the virtual and welded triplet groups $VL…

math.RT2026

The virtual singular twin monoid and group: presentations and representations

Carmen Caprau, Mohamad N. Nasser

In this article, we introduce the algebraic definitions and presentations of the virtual singular twin monoid and virtual singular twin group, denoted by $V S T M_{n}$ and $V S T_{n}$ , resp…

math.RT2025

Insights on the homogeneous $3$ -local representations of the twin groups

Mohamad N. Nasser

We provide a complete classification of the homogeneous $3$ -local representations of the twin group $T_{n}$ , the virtual twin group $V T_{n}$ , and the welded twin group $W T_{n}$ , for all…

math.RT2025

Algebraic and topological aspects of the singular twin group and its representations

Mohamad N. Nasser, Nafaa Chbili

In this article, we introduce the singular twin monoid and its corresponding group, constructed from both algebraic and topological perspectives. We then classify all complex homog…

math.RT2025

On the classification and irreducibility of $2$ -local representations of the twin group $T_{n}$

Taher I. Mayassi, Mohamad N. Nasser

We investigate the homogeneous $2$ -local representations of the twin group $T_{n}$ for all integers $n ⩾ 2$ . A complete classification is obtained, yielding three distinct fam…

math.RT2025

On representations of the multi-virtual braid group $M_{k} V B_{n}$ and the multi-welded braid group $M_{k} W B_{n}$

Vaibhav Keshari, Mohamad N. Nasser, Madeti Prabhakar

This paper classifies complex homogeneous $2$ -local representations of the multiple virtual braid group $M_{k} V B_{n}$ into $GL_{n} (C)$ for $n \geq 3$ and $k > 1$ , showing…

math.RT2025

On the irreducibility of singular braid group representations

Mohamad N. Nasser

In this article, we investigate the irreducibility of representations of the singular braid group on $n$ strands, denoted by $S B_{n}$ . We first show that all representations $ρ: SB_2…

math.RT2025

Twin groups representations

Mohamad N. Nasser

We construct two representations of the twin group $T_{n}, n \geq 2$ , namely $η_{1} : T_{n} \to Aut (F_{n})$ and $η_2: T_n \rightarrow \text{GL}_n(\mathbb{Z}[t^{\pm 1}…

math.RT2025

Matrix representations of the twisted virtual braid group and its extensions

Mohamad N. Nasser, Vaibhav Keshari, Madeti Prabhakar

This paper classifies complex local representations of the twisted virtual braid group, $T V B_{2}$ , into $GL_{3} (C)$ . It shows that such representations fall into eigh…

math.RT2025

On extensions of the standard representation of the braid group to the singular braid group

Mohamad N. Nasser

For an integer $n \geq 2$ , set $B_{n}$ to be the braid group on $n$ strands and $S B_{n}$ to be the singular braid group on $n$ strands. $S B_{n}$ is one of the important group extensions…

math.RT2025

Local Representations of the Flat Virtual Braid Group

Mohamad N. Nasser, Mohammad Y. Chreif, Malak M. Dally

We prove that any complex local representation of the flat virtual braid group, $F V B_{2}$ , into $G L_{2} (C)$ , has one of the types $λ_{i} : F V B_{2} \to G L_{2} (C)$ , $1…

math.RT2025

Classification of Homogeneous Local Representations of the Singular Braid Monoid

Taher I. Mayassi, Mohamad N. Nasser

For a natural number $n$ , denote by $B_{n}$ the braid group on $n$ strings and by $S M_{n}$ the singular braid monoid on $n$ strings. $S M_{n}$ is one of the most important extensions of $…

math.RT2024

On the Faithfulness of a Family of Representations of the Singular Braid Monoid $S M_{n}$

Mohamad N. Nasser

For $n \geq 2$ , let $G_{n}$ be a group and let $ρ : B_{n} \to G_{n}$ be a representation of the braid group $B_{n}$ . For a field $K$ and $a, b, c \in K$ , Bardakov, Chbi…

math.RT2023

The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_{n}$ in the cases $n = 3$ and $n = 4$

Mohamad N. Nasser

Let $C_{n}$ be the group of conjugating automorphisms. Valerij G. Bardakov defined a representation $ρ$ of $C_{n}$ , which is an extension of Lawrence-Krammer representation of the brai…

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…

On the structure of the singular triplet monoid and its virtual extension

Multi-welded twin groups

On Universal Virtual and Welded Braid Groups and Their Linear Representations

On representations of the triplet group and some of its extensions

The virtual singular twin monoid and group: presentations and representations

Insights on the homogeneous 3-local representations of the twin groups

Algebraic and topological aspects of the singular twin group and its representations

On the classification and irreducibility of 2-local representations of the twin group Tn​

On representations of the multi-virtual braid group Mk​VBn​ and the multi-welded braid group Mk​WBn​

On the irreducibility of singular braid group representations

Twin groups representations

Matrix representations of the twisted virtual braid group and its extensions

On extensions of the standard representation of the braid group to the singular braid group

Local Representations of the Flat Virtual Braid Group

Classification of Homogeneous Local Representations of the Singular Braid Monoid

On the Faithfulness of a Family of Representations of the Singular Braid Monoid SMn​

The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms Cn​ in the cases n=3 and n=4

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

Insights on the homogeneous $3$ -local representations of the twin groups

On the classification and irreducibility of $2$ -local representations of the twin group $T_{n}$

On representations of the multi-virtual braid group $M_{k} V B_{n}$ and the multi-welded braid group $M_{k} W B_{n}$

On the Faithfulness of a Family of Representations of the Singular Braid Monoid $S M_{n}$

The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_{n}$ in the cases $n = 3$ and $n = 4$