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On the compact real forms of the lie algebras of type E 6 and F 4

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Abstract

We give a construction of the compact real form of the Lie algebra of type E 6, using the finite irreducible subgroup of shape 33+3: SL3(3), which is isomorphic to a maximal subgroup of the orthogonal group Ω7(3). In particular we show that the algebra is uniquely determined by this subgroup. Conversely, we prove from first principles that the algebra satisfies the Jacobi identity, and thus give an elementary proof of existence of a Lie algebra of type E 6. The compact real form of F 4 is exhibited as a subalgebra.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queen Mary University of London, London, UK

    R. A. Wilson

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  1. R. A. Wilson
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Correspondence to R. A. Wilson.

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Original Russian Text Copyright © 2013 Wilson R.A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 1, pp. 208–224, January–February, 2013.

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Wilson, R.A. On the compact real forms of the lie algebras of type E 6 and F 4 . Sib Math J 54, 159–172 (2013). https://doi.org/10.1134/S0037446613010205

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  • DOI: https://doi.org/10.1134/S0037446613010205

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