Classification of Homogeneous Local Representations of the Singular Braid Monoid

Taher I. Mayassi; Mohamad N. Nasser

paper

Classification of Homogeneous Local Representations of the Singular Braid Monoid

arXiv:2501.13404

Abstract

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 $B_{n}$ . In [13], Y. Mikhalchishina classified all homogeneous $2$ -local representations of $B_{n}$ for all $n \geq 3$ . In this article, we extend the result of Mikhalchishina in two ways. First, we classify all homogeneous $3$ -local representations of $B_{n}$ for all $n \geq 4$ . Second, we classify all homogeneous $2$ -local representations of $S M_{n}$ for all $n \geq 2$ and all homogeneous $3$ -local representations of $S M_{n}$ for all $n \geq 4$ .