English

On axial algebras with $3$ eigenvalues

Rings and Algebras 2024-10-04 v1

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 33 eigenvalues and the fusion law is the least restrictive, we describe 22-generated and 33-generated algebras and prove some of their general properties.

Keywords

Cite

@article{arxiv.2410.02034,
  title  = {On axial algebras with $3$ eigenvalues},
  author = {Vsevolod A. Afanasev},
  journal= {arXiv preprint arXiv:2410.02034},
  year   = {2024}
}

Comments

20 pages

R2 v1 2026-06-28T19:06:04.880Z