The magic square and symmetric compositions. II
type: Item
instance of: scholarly article
title: The magic square and symmetric compositions. II
zbMATH Open document ID: 1145.17005
DOI: 10.4171/RMI/486
author: Alberto Elduque
published in: Revista Matemática Iberoamericana
publication date: 2007-08-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1180728885
full work available at URL: https://eudml.org/doc/43583
review text: Summary: 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, is 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 is 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. Part I, see Rev. Mat. Iberoam. 20, No. 2, 475--491 (2004; Zbl 1106.17011).
Mathematics Subject Classification ID: 17B25
Mathematics Subject Classification ID: 17A75
zbMATH DE Number: 5177705
zbMATH Keywords: Freudenthal magic square
zbMATH Keywords: symmetric composition algebra
zbMATH Keywords: triality
zbMATH Keywords: exceptional Lie algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5177705