TY - JOUR
TI - On the Irreducibility of Fourth Dimensional Tuba's Representation of the Pure Braid Group on Three Strands
PY - 2018/07/31
Y2 - 2024/06/17
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 11
IS - 3
LA - en
DO - 10.29020/nybg.ejpam.v11i3.3273
UR - https://doi.org/10.29020/nybg.ejpam.v11i3.3273
SP - 682-701
AB - 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
ER -