Axial identities
Rings and Algebras
2025-11-24 v3
Abstract
The notions of idempotental identities and axial identities of axial algebras are introduced, in order to understand better some theorems of J.~Desmet, I.~Gorshkov, S.~Shpectorov, and A.~Staroletov about solid subalgebras; this approach produces generic examples, including an example of an axial algebra of Jordan type 1/2 with a Frobenius form having radical 0, which is neither Jordan nor a homomorphic image of a Matsuo algebra.
Cite
@article{arxiv.2508.16427,
title = {Axial identities},
author = {Louis Halle Rowen},
journal= {arXiv preprint arXiv:2508.16427},
year = {2025}
}
Comments
36 pages. Some misprints from previous versions corrected, and generic axial algebra refined