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The classification that has been an inspiration for over a century is the Cartan-Killing classification of finite-dimensional simple complex Lie algebras. This precedes Wedderburn theory. This is surely (?) the most significant classification.

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The classification that has been an inspiration for over a century is the Cartan-Killing classification of simple complex Lie algebras. This precedes Wedderburn theory. This is surely (?) the most significant classification.