(untitled) (European Journal of Pure and Applied Mathematics, 2018)
We consider Tuba’s representation of the pure braid group, %P_3 , given by the map φ :P_3GL(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 φ