A recent construction of Freudenthal's Magic Square by means of symmetric composition algebras will be reviewed. In dimension 8 there are two classes oi such algebras: para-IIurwitz and Okubo. and the relationship between the exceptional simple Lie algebras obtained from these two classes will be given. A natural invariant bilinear form will be defined and used to show that all the real central simple exceptional Lie algebras of type F and E do appear in the construction.
展开▼
