Freudenthal algebraIn algebra, Freudenthal algebras are certain Jordan algebras constructed from composition algebras.DefinitionSuppose that C is a composition algebra over a field F and a is a diagonal matrix in GLn. 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 Ta=''aX''. A Freudenthal algebra is any twisted form of a reduced Freudental algebra.