Searching for groups related to pseudo-composition algebras

TL;DR

This paper investigates a specific subclass of axial algebras called pseudo-composition algebras, focusing on their automorphism groups using the group-algebra correspondence to understand their structure.

Contribution

It introduces a study of automorphism subgroups of idempotent-generated pseudo-composition algebras within the axial algebra framework.

Findings

Identification of automorphism subgroups

Application of group-algebra correspondence

Enhanced understanding of pseudo-composition algebra structure

Abstract

We study the class of idempotent-generated pseudo-composition algebras, which is a subclass of the family of axial algebras. More specifically, we utilise the group-algebra correspondence, natural to the axial framework in order to study some automorphism subgroups of such pseudo-composition algebras.