Abstract An Alexander pair ( f 1 , f 2 ) and an ( f 1 , f 2 ) -twisted 2-cocycle can be used to define a generalization of twisted Alexander matrices and twisted Alexander invariants. In this paper, we introduce row relation maps with respect to Alexander pairs, and we show the following two properties: First, a row relation map gives a linear relation among the row vectors of an ( f 1 , f 2 ) -twisted Alexander matrix. Second, given an ( f 1 , f 2 ) -twisted 2-cocycle and a row relation map, we can obtain a shadow quandle 2-cocycle and additionally a shadow quandle cocycle invariant. We also discuss the fact that a generalized quandle cocycle invariant is a shadow quandle cocycle invariant.

中文翻译：

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扭曲的亚历山大矩阵和影子 quandle 2-cocycle 的行关系

摘要 亚历山大对 ( f 1 , f 2 ) 和 ( f 1 , f 2 ) -twisted 2-cocycle 可用于定义扭曲亚历山大矩阵和扭曲亚历山大不变量的推广。在本文中，我们介绍了关于 Alexander 对的行关系映射，我们展示了以下两个性质：首先，行关系映射给出了 ( f 1 , f 2 ) -twisted Alexander 矩阵的行向量之间的线性关系. 其次，给定一个 ( f 1 , f 2 ) -twisted 2-cocycle 和一个行关系图，我们可以得到一个 shadow quandle 2-cocycle 和一个 shadow quandle cocycle 不变量。我们还讨论了这样一个事实，即广义 quandle cocycle 不变量是影子 quandle cocycle 不变量。