The Magic Square and Symmetric Compositions II

Details The Magic Square and Symmetric Compositions II The Magic Square and Symmetric Compositions II

2005-07-14

arxiv.org/abs/math/0507282v1

Mathematics

Representation Theory

24 pages. To appear in Rev. Mat. Iberoamericana

Scientific paper

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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