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Semisimple Lie Algebra**

A Lie algebra \(L\) is called 'semisimple' if it has ideals \((\mathfrak{g}_i)_{i\in I}\) such that each \(\mathfrak{g}_i\) is simple and \(L\) is their direct sum, \(L=\bigoplus_{i\in I}\mathfrak{g}_i\).