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Krammer's Representation of the Pure Braid Group, 𠑃 3

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  • Mohammad N. Abdulrahim
  • Madline Al-Tahan

Abstract

We consider Krammer's representation of the pure braid group on three strings: 𠑃 3 → ð º ð ¿ ( 3 , ð ‘ [ ð ‘¡ ± 1 , ð ‘ž ± 1 ] ) , where ð ‘¡ and ð ‘ž are indeterminates. As it was done in the case of the braid group, ð µ 3 , we specialize the indeterminates ð ‘¡ and ð ‘ž to nonzero complex numbers. Then we present our main theorem that gives us a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of Krammer's representation of the pure braid group, 𠑃 3 .

Suggested Citation

  • Mohammad N. Abdulrahim & Madline Al-Tahan, 2010. "Krammer's Representation of the Pure Braid Group, 𠑃 3," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-10, June.
    • Handle: RePEc:hin:jijmms:806502
    DOI: 10.1155/2010/806502
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