Terwilliger algebras constructed from Cayley tables of finite Bol loops

TL;DR

This paper investigates the structure of Terwilliger algebras derived from Cayley tables of Bol loops, providing insights into their algebraic properties and necessary conditions for quasigroups to be Bol loops.

Contribution

It introduces the construction of Terwilliger algebras from Bol loops and establishes necessary conditions for quasigroups to qualify as Bol loops.

Findings

Describes Terwilliger algebras of four-class Latin-square association schemes

Provides necessary algebraic conditions for Bol loops

Links algebraic properties to quasigroup classifications

Abstract

We describe the Terwilliger algebras of the four-class Latin-square association schemes arising from Cayley tables of Bol loops. We give some necessary conditions involving Terwilliger algebras for a quasigroup to be a Bol loop.