Decomposition of the regular representation for dihedral quandles

TL;DR

This paper analyzes how the regular representation of dihedral quandles can be broken down into simpler, irreducible components, enhancing understanding of their algebraic structure.

Contribution

It provides a detailed decomposition of the regular quandle representation for dihedral quandles, which was not previously established.

Findings

Decomposition into irreducible subrepresentations achieved

Explicit structure of subrepresentations characterized

Advances understanding of dihedral quandle algebraic properties

Abstract

We decompose the regular quandle representation of a dihedral quandle $\mathcal{R}_n$ into irreducible quandle subrepresentations.