The Open Mathematics Journal

2012, 5 : 15-18
Published online 2012 July 13. DOI: 10.2174/1874117701205010015
Publisher ID: TOMATJ-5-15

On the Irreducibility of Wada's Representation of the Pure Braid Group, P

Ghenwa H. Abboud and Mohammad N. Abdulrahim
Department of Mathematics, Beirut Arab University, P.O. Box 11-5020, Beirut, Lebanon.

ABSTRACT

We consider the reduced Wada's representation of the pure braid group, namely p4>→GL3(Z[t1±1,t2±1,t3±1,t4±1]). We then specialize the parameters t1,t2,t3,t4 to nonzero complex numbers Z1,Z2,Z3,Z4. Our main theorem asserts that the reduced Wada's representation φ4 :p 4→GL3(C), is reducible if and only if Z21, = Z 22 = Z23 = Z24.

Keywords:

Pure braid group, Wada's representation, irreducible.