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On the representations of the braid group and the welded braid group

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Title: On the representations of the braid group and the welded braid group

Authors: Rana S. Kahil, Mohammad N. Abdulrahim

Journal: Journal of Prime Research in Mathematics

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
Y 2020-07-01 2021-06-30

Publisher: Abdus Salam School of Mathematical Sciences, GC University

Country: Pakistan

Year: 2023

Volume: 19

Issue: 1

Language: English

Keywords: representationsbraid groupwelded braid group

Categories
Braid Group (1) Representations (1) Topology (93) Algebraic Structures (6) Group Theory (67)

Abstract

We study the composition of F. R. Cohen’s map Bn → Bnk with the standard representation of Bnk, where Bn is the braid group on n strings. We prove that the obtained representation of Bn is isomorphic to the direct sum of k copies of the standard representation of Bn. A similar work is done for the welded braid group 𝓌Bn.

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