Abstract
We develop techniques of connections of roots for split Lie algebras with symmetric root systems. We show that any of such algebras L is of the form L = \( \mathcal{U} \) + Σ j I j with \( \mathcal{U} \) a subspace of the abelian Lie algebra H and any I j a well described ideal of L, satisfying [I j , I k ] = 0 if j ≠ k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split Lie algebra with a symmetric root system and having all its nonzero roots connected.
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Martín, A.J.C. On split Lie algebras with symmetric root systems. Proc Math Sci 118, 351–356 (2008). https://doi.org/10.1007/s12044-008-0027-3
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DOI: https://doi.org/10.1007/s12044-008-0027-3