The magic square and symmetric compositions. II (Q997808): Difference between revisions

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).