A note on quadratic Jordan algebras of degree 3

Racine, M. L.

doi:10.1090/S0002-9947-1972-0304447-0

A note on quadratic Jordan algebras of degree $3$
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by M. L. Racine

Trans. Amer. Math. Soc. 164 (1972), 93-103

DOI: https://doi.org/10.1090/S0002-9947-1972-0304447-0

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Abstract:

McCrimmon has defined a class of quadratic Jordan algebras of degree 3 obtained from a cubic form, a quadratic mapping and a base point. The structure of such an algebra containing no absolute zero-divisor is determined directly. A simple proof of Springer’s Theorem on isomorphism of reduced simple exceptional quadratic Jordan algebras is given.

References

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