Multivariate Alexander quandles. V: Constructing the medial quandle of a link (Q6629557)

This paper is the fifth in a series by the author focusing on Alexander modules and quandles. It explores how the medial quandle of a classical or virtual link can be constructed using the peripheral structure of the reduced Alexander module, specifically leveraging the recently introduced module's peripheral elements. For knots, however, these peripheral elements play no role in the construction. Consequently, the author extends Joyce's result to virtual knots, showing that the medial quandle of a classical knot corresponds to the standard Alexander quandle on the Alexander invariant of the knot [\textit{D. Joyce}, J. Pure Appl. Algebra 23, 37--65 (1982; Zbl 0474.57003)].