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 . 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.
2020 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors are grateful to the anonymous referee for useful remarks.