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arXiv · 2305.10958

On Jordan algebras that are factors of Matsuo algebras

Ilya Gorshkov·Andrey Mamontov·Alexey Staroletov
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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 F is a field of characteristic 0, then there exist infinitely many primitive axial algebras of Jordan type 1/2 over F that are not factors of Matsuo algebras. As an illustrative example, we prove this for an exceptional Jordan algebra over F.

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Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov. 2023-05-18. On Jordan algebras that are factors of Matsuo algebras. https://arxiv.org/abs/2305.10958

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