On the Irreducibility of Fourth Dimensional Tuba's Representation of the Pure Braid Group on Three Strands
2018 ◽
Vol 11
(3)
◽
pp. 682-701
Keyword(s):
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
2010 ◽
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2000 ◽
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pp. 515-524
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1981 ◽
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2007 ◽
Vol 49
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pp. 431-447
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