2022/02/22 by Yuta Taniguchi, Taniguchi, Yuta · 1 citation
Mathematics · #57K10 #57K12 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2202.10754
openalex publication_date 2022/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A quandle is an algebraic structure whose axioms correspond to the Reidemeister moves of knot theory. S. Kamada introduced the notion of a quandle with a good involution, which is later called a symmetric quandle. We are interested in the algebraic structure of symmetric quandles. Given a group G, an element z and a certain subgroup H, one can obtain the quandle. D. Joyce showed that every quandle is isomorphic to the disjoint union of such quandles. In this paper, given a group G, elements z,r in G and a certain subgroup H, we construct a symmetric quandle. Futhermore, we show that every symmetric quandle is isomorphic to the disjoint union of such quandles.