TY - JOUR

T1 - On Jordan algebras that are factors of Matsuo algebras

AU - Gorshkov, Ilya

AU - Mamontov, Andrey

AU - Staroletov, Alexey

N1 - The work is supported by Mathematical Center in Akademgorodok under agreement No.075-15 2022-281 with the Ministry of Science and Higher Education of the Russian Federation

PY - 2025/1/14

Y1 - 2025/1/14

N2 - 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~$\mathbb{F}$.

AB - 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~$\mathbb{F}$.

UR - https://www.mendeley.com/catalogue/4124a0e7-0640-3e0e-966b-34d599eb042c/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85216410890&origin=inward&txGid=e69af6d84b2ac0b14b5a7ca977b12daa

UR - https://elibrary.ru/item.asp?id=67649901

U2 - 10.24330/ieja.1488467

DO - 10.24330/ieja.1488467

M3 - Article

SP - 70

EP - 90

JO - International Electronic Journal of Algebra

JF - International Electronic Journal of Algebra

SN - 1306-6048

ER -