On the Irreducibility of Fourth Dimensional Tuba's Representation of the Pure Braid Group on Three Strands

Authors

  • Hasan A. Haidar Beirut Arab University
  • Mohammad N. Abdulrahim Department of Mathematics Professor Beirut Arab UNiversity P.O. Box: 11-5020 Beirut, Lebanon

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i3.3273

Keywords:

Braid group, pure braid group, irreducible

Abstract

We consider Tuba's representation of the pure braid group, $%P_{3} $, given by the map $\phi :P_{3}\longrightarrow GL(4,F)$, where $F$ is an algebraically closed field. After, specializing the indeterminates used in defining the representation to non- zero complex numbers, we find sufficient conditions that guarantee the irreducibility of Tuba's representation of the pure braid group $P_{3}$ with dimension $d=4$. Under further restriction for the complex specialization of the indeterminates, we get a necessary and sufficient condition for the irreducibility of $\phi

Author Biographies

  • Hasan A. Haidar, Beirut Arab University

    Department of Mathematics

    Ph.D.  student

  • Mohammad N. Abdulrahim, Department of Mathematics Professor Beirut Arab UNiversity P.O. Box: 11-5020 Beirut, Lebanon

    Department of Mathematics

    Professor

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Published

2018-07-31

Issue

Section

Mathematical Biosciences

How to Cite

On the Irreducibility of Fourth Dimensional Tuba’s Representation of the Pure Braid Group on Three Strands. (2018). European Journal of Pure and Applied Mathematics, 11(3), 682-701. https://doi.org/10.29020/nybg.ejpam.v11i3.3273