# nLab Élie Cartan

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Élie Joseph Cartan was a French differential geometer. His results include the classification of complex semisimple Lie algebras (“Cartan classification”), extension of these results to a class of symmetric spaces, the proof of the Lie–Cartan theorem (after Serre sometimes called “Lie's third theorem”) on integration of Lie algebras to Lie groups (Lie proved just the integration to local Lie groups), the method of moving frames, the introduction of Cartan’s connection, numerous results in Riemannian geometry, results related to the formal integrability of PDEs (Cartan involutive equations, Pfaffian system), etc.

Father of Henri Cartan.

category: people

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