On the Irreducibility of Artin's Group of Graphs
Keyword(s):
We consider the graph $E_{3,1}$ with three generators $\sigma_1, \sigma_2, \delta$, where $\sigma_1$ has an edge with each of $\;\sigma_2$ and $\;\delta$. We then define the Artin group of the graph $E_{3,1}$ and consider its reduced Perron representation of degree three. After we specialize the indeterminates used in defining the representation to non-zero complex numbers, we obtain a necessary and sufficient condition that guarantees the irreducibility of the representation.<br />
1999 ◽
Vol 19
(5)
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pp. 1221-1231
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2018 ◽
Vol 11
(3)
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pp. 682-701
2010 ◽
Vol 2010
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pp. 1-10
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2017 ◽
Vol E100.A
(12)
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pp. 2764-2775
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