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On Jordan algebras that are factors of Matsuo algebras (2305.10958v2)
Published 18 May 2023 in math.RA and math.GR
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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