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Ideal (Lie Algebra)**

Given a Lie algebra \(\mathfrak{g}\), a subalgebra \(\mathfrak{h}\subseteq\mathfrak{g}\) is called an ideal if \([\mathfrak{h},\mathfrak{g}]\subseteq\mathfrak{h}\), where \([\mathfrak{h},\mathfrak{g}]\) is the standard product of subalgebras. The subalgebras \(\mathfrak{g},\{0\}\) are ideals for any Lie algebra \(\mathfrak{g}\) and so are called 'trivial'.