Infinitely many two-variable generalisations of the Alexander-Conway polynomial
Infinitely many two-variable generalisations of the Alexander-Conway polynomial
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亚历山大-康威多项式的无穷多个二变量推广
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
J. Links
中科院分区：
文献类型：
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作者：
D. D. Wit;Atsushi Ishii;J. Links
我们表明，Alexander-Conway多项式获得-可通过一个特定的一个变量减少每个两个变量的链接-古尔德不变LG m，1，其中m是一个正整数。因此，存在无穷多个双变量的一般化。这个结果并不明显，因为在约化中，用于定义LG m，1的辫群生成元的表示不满足二阶特征恒等式，除非m = 1。为了证明LG m，1的单变量约化满足定义的绞关系，我们计算了量子迹的核。AMS分类57 M25、57 M27; 17 B37、17 B81
We show that the Alexander-Conway polynomialis obtain- able via a particular one-variable reduction of each two-variable Links- Gould invariant LG m,1 , where m is a positive integer. Thus there exist infinitely many two-variable generalisations of �. This result is not obvi- ous since in the reduction, the representation of the braid group generator used to define LG m,1 does not satisfy a second-order characteristic identity unless m = 1. To demonstrate that the one-variable reduction of LG m,1 satisfies the defining skein relation of �, we evaluate the kernel of a quan- tum trace. AMS Classification 57M25, 57M27; 17B37, 17B81