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University of Bristol; Heilbronn Institute for Mathematical Research, Bristol; University of Birmingham; University of ChesterPublication Date
2021-12-22
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Motivated 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.Citation
McInroy, J., & Shpectorov, S. (2022). Split spin factor algebras. Journal of Algebra, 595, 380–397. https://doi.org/10.1016/j.jalgebra.2021.12.022Publisher
ElsevierJournal
Journal of AlgebraAdditional Links
https://www.sciencedirect.com/science/article/abs/pii/S0021869321006268?via%3Dihubhttps://research-information.bris.ac.uk/en/publications/split-spin-factor-algebras
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ArticleISSN
0021-8693ae974a485f413a2113503eed53cd6c53
10.1016/j.jalgebra.2021.12.022
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