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标题：Krammer's Representation of the Pure Braid Group, <svg style="vertical-align:-4.67648pt;width:21.9125px;" id="M1" height="20.5875" version="1.1" viewBox="0 0 21.9125 20.5875" width="21.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.5875)"> <g transform="translate(72,-55.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.24)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑃</tspan> </text> <text transform="matrix(1,0,0,-1,-61.3,55.76)"> <tspan style="font-size: 12.55px; " x="0" y="0">3</tspan> </text> </g> </g> </svg>
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作者：Mohammad N. Abdulrahim ; Madline Al-Tahan
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2010
卷号：2010
DOI：10.1155/2010/806502
出版社：Hindawi Publishing Corporation
摘要：We consider Krammer's representation of the pure braid group on three strings: 𝑃3→𝐺𝐿(3,𝑍[𝑡±1,𝑞±1]), where 𝑡 and 𝑞 are indeterminates. As it was done in the case of the braid group, 𝐵3, we specialize the indeterminates 𝑡 and 𝑞 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, 𝑃3.