Why is it that if the roots of a Lie algebra form angles of 90 degrees, the Lie algebra is not simple? Is it because the said roots commute with each other and so the Lie algebra can be broken down to nontrivial two-sided ideals? If that is the case, then why are these roots not a part of the Cartan subalgebra (maximal subspace of commuting Hermitian generators)?
2026-03-25 12:48:46.1774442926
Root system of Lie algebra: right angle => not simple?
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