On the Irreducibility of Fourth Dimensional Tuba's Representation of the Pure Braid Group on Three Strands

Hasan A. Haidar, Mohammad N. Abdulrahim

Abstract

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

Keywords

Braid group; pure braid group; irreducible

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