High Quality Content by WIKIPEDIA articles! In mathematics, the Maurer–Cartan form for a Lie group G is a distinguished differential one-form on G that carries within itself the basic infinitesimal information about the structure of G. It was much used by Elie Cartan as a basic ingredient of his method of moving frames, and bears his name together with that of Ludwig Maurer. As a one-form, the Maurer–Cartan form is peculiar in that it takes its values in the Lie algebra associated to the Lie group G. The Lie algebra is identified with the tangent space of G at the identity, denoted TeG. The Maurer–Cartan form ? is thus a one-form defined globally on G which is a linear mapping of the tangent space TgG at each g ? G into TeG.

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