JournalsrmiVol. 23, No. 1pp. 57–84

The Magic Square and Symmetric Compositions II

  • Alberto Elduque

    Universidad de Zaragoza, Spain
The Magic Square and Symmetric Compositions II cover
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Abstract

The construction of Freudenthal's Magic Square, which contains the exceptional simple Lie algebras of types F4,E6,E7F_4,E_6,E_7 and E8E_8, 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 sl2\mathfrak{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 sl2\mathfrak{sl}_2 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

DOI 10.4171/RMI/486