Abstract
The recent development of superstring theory (1) has drawn attention to the potential importance of the exceptional Lie algebras (particularly E/sub 6/ and E/sub 8/) in a future unified theory. The paper consists of three parts. In the first, the authors consider normed algebras and the properties of their transformations. In the second they give the construction of the magic square and the corresponding commutation relations. The construction is anticipated by two symmetric constructions, the symbiosis of which it is. In the final part, the exceptional algebras of the series E are decomposed. The proofs of the Jacobi identities and the identification of the algebras in the magic square are omitted since the calculations are lengthy.
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