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arXiv · 2410.02034

On axial algebras with $3$ eigenvalues

Vsevolod A. Afanasev
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Abstract

We study axial algebras, that is, commutative non-associative algebras generated by idempotents whose adjoint actions are semisimple and obey a fusion law. Considering the case, when said adjoint actions having $3$ eigenvalues and the fusion law is the least restrictive, we describe $2$-generated and $3$-generated algebras and prove some of their general properties.

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Vsevolod A. Afanasev. 2024-10-02. On axial algebras with $3$ eigenvalues. https://doi.org/10.1016/j.jalgebra.2026.06.008.

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