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

Vol. 11 No. 3: (July 2018)

Section

Mathematical Biosciences

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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