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The Magic Square and Symmetric Compositions II

Alberto Elduque
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Abstract

The construction of Freudenthal's Magic Square, which contains the exceptional simple Lie algebras, 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 sl(2). 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 sl(2) and of its natural module.

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Alberto Elduque. 2005-07-14. The Magic Square and Symmetric Compositions II. https://arxiv.org/abs/math/0507282

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