@article{On the Irreducibility of Fourth Dimensional Tuba’s Representation of the Pure Braid Group on Three Strands_2018, place={Maryland, USA}, volume={11}, url={https://www.ejpam.com/index.php/ejpam/article/view/3273}, DOI={10.29020/nybg.ejpam.v11i3.3273}, abstractNote={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}, number={3}, journal={European Journal of Pure and Applied Mathematics}, year={2018}, month={Jul.}, pages={682–701} }