
Freudenthal algebra

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 GL"n"("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 T"a"="aX". A Freudenthal algebra is any twisted form of a reduced Freudental algebra.