On Jordan algebras that are factors of Matsuo algebras

Year 2024, Early Access, 1 - 21

Ilya Gorshkov Andrey Mamontov Alexey Staroletov

https://doi.org/10.24330/ieja.1488467

Abstract

We describe all finite connected 3-transposition groups whose Matsuo algebras have nontrivial factors that are Jordan algebras. As a corollary, we show that if $\mathbb{F}$ is a field of characteristic 0, then there exist
infinitely many primitive axial algebras of Jordan type $\frac{1}{2}$ over $\mathbb{F}$ that are not factors of Matsuo algebras. As an example, we prove this for an exceptional Jordan algebra over~$\mathbb{F}$.

Keywords

Axial algebra, Matsuo algebra, Jordan algebra, 3-transposition group

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