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arXiv · 2308.16450

Generalized sharped cubic form and split spin factor algebra

Vsevolod Gubarev·Farukh Mashurov·Alexander Panasenko
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Abstract

There is a well-known construction of a Jordan algebra via a sharped cubic form. We introduce a generalized sharped cubic form and prove that the split spin factor algebra is induced by this construction and satisfies the identity $((a,b,c),d,b) + ((c,b,d),a,b) + ((d,b,a),c,b) = 0$. The split spin factor algebras have recently appeared in the classification of 2-generated axial algebras of Monster type fulfilled by T. Yabe; their properties were studied by J. McInroy and S. Shpectorov.

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Vsevolod Gubarev, Farukh Mashurov, Alexander Panasenko. 2023-08-31. Generalized sharped cubic form and split spin factor algebra. https://doi.org/10.1080/00927872.2024.2317454

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