Freudenthal algebra
# 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 $X^Ta=aX.$ A Freudenthal algebra is any twisted form of a reduced Freudental algebra.

