Cubic subfields of exceptional simple Jordan algebras

Petersson, H. P.; Racine, M. L.

doi:10.1090/S0002-9939-1984-0735558-7

Cubic subfields of exceptional simple Jordan algebras
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by H. P. Petersson and M. L. Racine PDF

Proc. Amer. Math. Soc. 91 (1984), 31-36 Request permission

Abstract:

Let $E/k$ be a cubic field extension and $J$ a simple exceptional Jordan algebra of degree 3 over $k$. Then $E$ is a reducing field of $J$ if and only if $E$ is isomorphic to a (maximal) subfield of some isotope of $J$. If $k$ has characteristic not 2 or 3 and contains the third roots of unity then every simple exceptional Jordan division algebra of degree 3 over $k$ contains a cyclic cubic subfield.

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