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In mathematics, the Maurer–Cartan form for a Lie group is a distinguished differential one-form on that carries the basic infinitesimal information about the structure of . It was much used by Élie 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 . The Lie algebra is identified with the tangent space of at the identity, denoted . The Maurer–Cartan form is thus a one-form defined globally on which is a linear mapping of the tangent space at each into . It is given as the pushforward of a vector in along the left-translation in the group: : ==Motivation and interpretation== A Lie group acts on itself by multiplication under the mapping : A question of importance to Cartan and his contemporaries was how to identify a principal homogeneous space of . That is, a ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maurer–Cartan form」の詳細全文を読む スポンサード リンク
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