Row relations of twisted Alexander matrices and shadow quandle 2-cocycles
The authors continue their study of Alexander pairs \((f_1,f_2)\) and \((f_1 , f_2 )\)-twisted 2-cocycles, see [\textit{A. Ishii} and \textit{K. Oshiro}, ``Twisted derivatives with Alexander pairs for quandles'', Preprint]. 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, the authors introduce row relation maps with respect to Alexander pairs, and 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, the authors obtain a shadow quandle 2-cocycle and additionally a shadow quandle cocycle invariant. The authors also discuss the fact that a generalized quandle cocycle invariant is a shadow quandle cocycle invariant.
scientific article; zbMATH DE number 7401499
scientific article