The equation [B,(A-1)(A,B)] = 0 and virtual knots and links
The equation [B,(A-1)(A,B)] = 0 and virtual knots and links
复制标题
方程 [B,(A-1)(A,B)] = 0 和虚拟结和链接
DOI：
10.4064/fm184-0-2
复制
发表时间：
2004
影响因子：
0.6
通讯作者：
R. Fenn
中科院分区：
文献类型：
--
作者：
S. Budden;R. Fenn
设A，B是环R的可逆、非交换元，假设A−1也是可逆的，且满足称为基本方程的方程[B，(A−1)(A，B)]=0。然后，这定义了代数F={A，B|[B，(A−1)(A，B)]=0}的表示。然后，可以为(虚拟)结或环的任何图定义不变的R-模。这使得以前已知的关系的数量减半，并允许我们在R是四元数的情况下给出一个完整的解。
Let A, B be invertible, non-commuting elements of a ring R. Suppose that A − 1 is also invertible and that the equation [B, (A − 1)(A,B)] = 0 called the fundamental equation is satisfied. Then this defines a representation of the algebra F = {A,B | [B, (A − 1)(A,B)] = 0}. An invariant R-module can then be defined for any diagram of a (virtual) knot or link. This halves the number of previously known relations and allows us to give a complete solution in the case when R is the quaternions.