McInroy, JustinShpectorov, Sergey2022-07-282022-07-282021-12-22McInroy, J., & Shpectorov, S. (2022). Split spin factor algebras. Journal of Algebra, 595, 380–397. https://doi.org/10.1016/j.jalgebra.2021.12.0220021-869310.1016/j.jalgebra.2021.12.022http://hdl.handle.net/10034/627049Motivated by Yabe's classification of symmetric $2$-generated axial algebras of Monster type \cite{yabe}, we introduce a large class of algebras of Monster type $(\alpha, \frac{1}{2})$, generalising Yabe's $\mathrm{III}(\alpha,\frac{1}{2}, \delta)$ family. Our algebras bear a striking similarity with Jordan spin factor algebras with the difference being that we asymmetrically split the identity as a sum of two idempotents. We investigate the properties of these algebras, including the existence of a Frobenius form and ideals. In the $2$-generated case, where our algebra is isomorphic to one of Yabe's examples, we use our new viewpoint to identify the axet, that is, the closure of the two generating axes.https://creativecommons.org/licenses/by-nc-nd/4.0/Spin factorJordan algebraaxial algebraArticleJournal of Algebra