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April, 2007 The Magic Square and Symmetric Compositions II
Alberto Elduque
Rev. Mat. Iberoamericana 23(1): 57-84 (April, 2007).


The construction of Freudenthal's Magic Square, which contains the exceptional simple Lie algebras of types $F_4,E_6,E_7$ and $E_8$, 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 $\mathfrak{sl}_2$. 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 $\mathfrak{sl}_2$ and of its natural module.


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Alberto Elduque. "The Magic Square and Symmetric Compositions II." Rev. Mat. Iberoamericana 23 (1) 57 - 84, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1145.17005
MathSciNet: MR2351126

Primary: 17B25
Secondary: 17A75

Keywords: exceptional Lie algebra , Freudenthal magic square , symmetric composition algebra , triality

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 1 • April, 2007
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