The construction of Freudenthal's Magic Square, which contains the exceptional simple Lie algebras of types and , in terms of symmetric composition algebras is further developed here. The para-Hurwitz algebras, which form a subclass of the symmetric composition algebras, will be defined, in the split case, in terms of the natural two dimensional module for the simple Lie algebra . As a consequence, it will be shown how all the Lie algebras in Freudenthal's Magic Square can be constructed, in a unified way, using copies of and of its natural module.
Cite this article
Alberto Elduque, The Magic Square and Symmetric Compositions II. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 57–84