The Magic Square and Symmetric Compositions II

The construction of Freudenthal's Magic Square, which contains theexceptional simple Lie algebras, in terms of symmetric composition algebras isfurther developed here. The para-Hurwitz algebras, which form a subclass of thesymmetric composition algebras, will be defined, in the split case, in terms ofthe natural two dimensional module for the simple Lie algebra sl(2). As aconsequence, it will be shown how all the Lie algebras in Freudenthal's MagicSquare can be constructed, in a unified way, using copies of sl(2) and of itsnatural module.