Axial identities
arXiv:2508.16427
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.
36 pages. Some misprints from previous versions corrected, and generic axial algebra refined