Primitive 4-generated axial algebras of Jordan type

TL;DR

This paper establishes an upper bound of 81 dimensions for primitive 4-generated axial algebras of Jordan type, providing a significant constraint on their possible size.

Contribution

It proves that such axial algebras cannot exceed 81 dimensions, offering new limitations on their structure and classification.

Findings

Primitive 4-generated axial algebras of Jordan type are at most 81-dimensional.

Provides a key bound that aids in classification efforts.

Enhances understanding of the structure of axial algebras.

Abstract

We show that primitive 4-generated axial algebras of Jordan type are at most 81-dimensional.