On the Irreducibility of Perron Representations of Degrees 4 and 5

Authors

  • Malak M. Dally Department of Mathematics Beirut Arab University P.O. Box: 11-5020 Beirut, Lebanon
  • 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.v11i1.3199

Keywords:

Artin representation, braid group, Burau representation, graph, irreducibility

Abstract

We consider the graph En+1,1 with (n+1) generators σ1,...,σn, and δ, where σi has an edge with σi+1 for i=1,...,n+1, and σ1 has an edge with δ. We then define the Artin group of the graph En+1,1 for n=3 and n=4 and consider its reduced Perron's representation of degrees
four and five respectively. After we specialize the indeterminates used in defining the representation to non-zero complex numbers, we obtain necessary and sufficient
conditions that guarantee the irreducibility of the representations for n=3 and 4 .

Author Biographies

  • Malak M. Dally, Department of Mathematics Beirut Arab University P.O. Box: 11-5020 Beirut, Lebanon

    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

2018-01-30

Issue

Section

Mathematical Biosciences

How to Cite

On the Irreducibility of Perron Representations of Degrees 4 and 5. (2018). European Journal of Pure and Applied Mathematics, 11(1), 215-237. https://doi.org/10.29020/nybg.ejpam.v11i1.3199