A guide to self-distributive quasigroups, or latin quandles

TL;DR

This paper provides a comprehensive overview of self-distributive quasigroups, highlighting their relation to quandles and focusing on representation methods like loop isotopy and linear representation.

Contribution

It connects older results on quasigroups with modern quandle theory and emphasizes representation techniques as key tools for analysis.

Findings

Relation between self-distributive quasigroups and quandles clarified

Representation methods such as loop isotopy and linear representation detailed

Modern theory of quandles integrated with classical results

Abstract

We present an overview of the theory of self-distributive quasigroups, both in the two-sided and one-sided cases, and relate the older results to the modern theory of quandles, to which self-distributive quasigroups are a special case. Most attention is paid to the representation results (loop isotopy, linear representation, homogeneous representation), as the main tool to investigate self-distributive quasigroups.