M. N. Nasser

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20242026

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16 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

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.RT2026

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 $I^»_{i} : F V B_{2} \to G L_{2} (C)$ , $…

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

Twin groups representations

Mohamad N. Nasser

We construct two representations of the twin group $T_{n}, n \geq 2$ , namely $I^\cdot_{1} : T_{n} \to Aut (F_{n})$ and $Î·_2: T_n \rightarrow \text{GL}_n(\mathbb{Z}[t^{\pm…