Journal of Advances in Mathematics and Computer Science

Tuba’s Representation of the Pure Braid Group on Three Strands

Noura Y. Maanna

Department of Mathematics, Beirut Arab University, Lebanon.

Mohammad N. Abdulrahim *

Department of Mathematics, Beirut Arab University, Lebanon.

*Author to whom correspondence should be addressed.

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Abstract

We consider Tuba’s representation of the pure braid group, P₃, defined by the map Ψ: P₃ → GL(V ), where V is an algebraically closed field. We then specialize the indeterminates used in defining the representation to non- zero complex numbers. Our objective is to find necessary and sufficient conditions that guarantee the irreducibility of Tuba’s representations of the pure braid group P₃ with dimensions d = 2 and d = 3.

Keywords: Braid group, pure braid group

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