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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A note on quadratic Jordan algebras of degree $ 3$


Author: M. L. Racine
Journal: Trans. Amer. Math. Soc. 164 (1972), 93-103
MSC: Primary 17A15
MathSciNet review: 0304447
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0304447-0
PII: S 0002-9947(1972)0304447-0
Keywords: Quadratic Jordan algebras, cubic form, isomorphism, exceptional Jordan algebra
Article copyright: © Copyright 1972 American Mathematical Society