Radicals in flip subalgebras

TL;DR

This paper introduces methods to analyze the properties of flip subalgebras within Matsuo algebras, focusing on their simplicity and radical dimension, contributing to the understanding of axial algebra structures.

Contribution

It develops new techniques for determining key properties of flip subalgebras in Matsuo algebras, advancing the study of axial algebra classifications.

Findings

Methods for determining simplicity of flip subalgebras

Techniques for calculating the radical dimension

Enhanced understanding of axial algebra structures

Abstract

We develop methods for determining key properties (simplicity and the dimension of radical) of flip subalgebras in Matsuo algebras. These are interesting classes of commutative non-associative algebras that were introduced within the broader paradigm of axial algebras.