Lie’sche Sätze
Lie's third theorem
In mathematics, Lie's third theorem states that every finite-dimensional Lie algebra g over the real numbers is associated to a Lie group G. Historically, the third theorem referred to a different but related result. The two preceding theorems of Sophus Lie, restated in modern language, relate to the infinitesimal transformations of a transformation group acting on a smooth manifold. The third theorem on the list stated the Jacobi identity for the infinitesimal transformations of a local Lie group. Conversely, in the presence of a Lie algebra of vector fields, integration gives a local Lie group action. The result now known as the third theorem provides an intrinsic and global converse to the original theorem.
In der Mathematik stellen die Lie’schen Sätze, benannt nach Sophus Lie, den Zusammenhang zwischen Lie-Gruppen und Lie-Algebren her.
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In der Mathematik stellen die Lie’schen Sätze, benannt nach Sophus Lie, den Zusammenhang zwischen Lie-Gruppen und Lie-Algebren her.
In mathematics, Lie's third theorem states that every finite-dimensional Lie algebra g over the real numbers is associated to a Lie group G. Historically, the third theorem referred to a different but related result. The two preceding theorems of Sophus Lie, restated in modern language, relate to the infinitesimal transformations of a transformation group acting on a smooth manifold. The third theorem on the list stated the Jacobi identity for the infinitesimal transformations of a local Lie group. Conversely, in the presence of a Lie algebra of vector fields, integration gives a local Lie group action. The result now known as the third theorem provides an intrinsic and global converse to the original theorem.
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