Connected Quandles Associated with Pointed Abelian Groups
Rings and Algebras
2016-11-15 v1 Geometric Topology
Abstract
A quandle is a self-distributive algebraic structure that appears in quasi-group and knot theories. For each abelian group A and c \in A we define a quandle G(A, c) on \Z_3 \times A. These quandles are generalizations of a class of non-medial Latin quandles defined by V. M. Galkin so we call them Galkin quandles. Each G(A, c) is connected but not Latin unless A has odd order. G(A, c) is non-medial unless 3A = 0. We classify their isomorphism classes in terms of pointed abelian groups, and study their various properties. A family of symmetric connected quandles is constructed from Galkin quandles, and some aspects of knot colorings by Galkin quandles are also discussed.
Keywords
Cite
@article{arxiv.1107.5777,
title = {Connected Quandles Associated with Pointed Abelian Groups},
author = {W. Edwin Clark and Mohamed Elhamdadi and Xiang-dong Hou and Masahico Saito and Timothy Yeatman},
journal= {arXiv preprint arXiv:1107.5777},
year = {2016}
}