Classification of Homogeneous Local Representations of the Singular Braid Monoid

2025/01/23 by Taher I. Mayassi, Mayassi, Taher I., Mohamad N. Nasser +1 · 6 citations
Computer Science · Mathematics · #20F36 #Advanced Algebra and Logic #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2501.13404

openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a natural number n, denote by B_n the braid group on n strings and by SM_n the singular braid monoid on n strings. SM_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 ≥ 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 ≥ 4. Second, we classify all homogeneous 2-local representations of SM_n for all n≥ 2 and all homogeneous 3-local representations of SM_n for all n≥ 4.

Cited by

• 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 T_n
• On the irreducibility of singular braid group representations
• On representations of the multi-virtual braid group M_kVB_n and the multi-welded braid group M_kWB_n
• Twin groups representations
• Matrix representations of the twisted virtual braid group and its extensions

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• A Faithful Representation of the Singular Braid Monoid on Three Strands
• On representations of the multi-virtual braid group M_kVB_n and the multi-welded braid group M_kWB_n
• Extensions of braid group representations to the monoid of singular braids
• On extensions of the standard representation of the braid group to the singular braid group