Rack Representations and Connections with groups representations

TL;DR

This paper explores the algebraic properties of racks and their representation theory, establishing a link with group representations to facilitate the application of group theory techniques to racks.

Contribution

It introduces a correspondence between irreducible strong rack representations and irreducible group representations, bridging rack theory and group representation theory.

Findings

Established a correspondence between rack and group irreducible representations.

Connected algebraic properties of racks with their representation theory.

Facilitated the use of group techniques in rack analysis.

Abstract

In this paper we study some algebraic properties of the rack structure as well as the representation theory of it, following the ideas given by M. Elhamdadi and E. M. Moutuou in \cite{Elhamdadi}. We establish a correspondence between the irreducible strong representations of a finite and connected rack with the irreducible representation of its finite enveloping group which allows to use techniques of the latter topic in the other setting.