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There is a well-known construction of a Jordan algebra via a sharped cubicform. We introduce a generalized sharped cubic form and prove that the splitspin 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 factoralgebras have recently appeared in the classification of 2-generated axialalgebras of Monster type fulfilled by T. Yabe; their properties were studied byJ. McInroy and S. Shpectorov.

Generalized sharped cubic form and split spin factor algebra