In algebra, Freudenthal algebras are certain Jordan algebras constructed from composition algebras.
Definition
Suppose that C is a composition algebra over a field F and a is a diagonal matrix in GLn(F). A reduced Freudenthal algebra is defined to be a Jordan algebra equal to the set of 3 by 3 matrices X over C such that XTa=aX. A Freudenthal algebra is any twisted form of a reduced Freudental algebra.
References
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