# On primitive axial algebras of Jordan type

## TL;DR

This paper reviews primitive axial algebras of Jordan type, explores their connections with 3-transposition groups and Matsuo algebras, and proves the existence of Frobenius forms for these algebras across all parameters.

## Contribution

It provides an overview of the current understanding and establishes that primitive axial algebras of Jordan type admit Frobenius forms for any parameter.

## Key findings

- Primitive axial algebras of Jordan type half are connected to 3-transposition groups.
- Matsuo algebras are related to these axial algebras.
- Frobenius forms exist for primitive axial algebras of Jordan type for all parameters.

## Abstract

In this note we give an overview of our knowledge regarding primitive axial algebras of Jordan type half and connections between $3$-transposition groups and Matsuo algebras. We also show that primitive axial algebras of Jordan type $\eta$ admit a Frobenius form, for any $\eta$.