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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 1, Pages 208–224
(Mi smj2414)
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This article is cited in 2 scientific papers (total in 2 papers)
On the compact real forms of the Lie algebras of type $E_6$ and $F_4$
R. A. Wilson School of Mathematical Sciences, Queen Mary University of London, London, UK
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 $3^{3+3}:\operatorname{SL}_3(3)$, which is isomorphic to a maximal subgroup of the orthogonal group $\Omega_7(3)$. 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.
Keywords:
Lie algebra, compact real form.
Received: 11.09.2012
Citation:
R. A. Wilson, “On the compact real forms of the Lie algebras of type $E_6$ and $F_4$”, Sibirsk. Mat. Zh., 54:1 (2013), 208–224; Siberian Math. J., 54:1 (2013), 159–172
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https://www.mathnet.ru/eng/smj2414 https://www.mathnet.ru/eng/smj/v54/i1/p208
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Abstract page: | 180 | Full-text PDF : | 72 | References: | 25 | First page: | 3 |
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