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

Authors

  • Rana S. Kahil Department of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon.
  • Mohammad N. Abdulrahim Department of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon.

Keywords:

Braid group, common fixed point, Welded Braid group, Cohen. 2010 MSC, Primary, 20F36

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 ????Bn.

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Published

2023-06-30

Issue

Vol. 19 No. 1 (2023): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

On the representations of the braid group and the welded braid group. (2023). Journal of Prime Research in Mathematics, 19(1), 34 – 43. https://jprm.sms.edu.pk/index.php/jprm/article/view/206