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 it 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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