Lie Groups and Lie Algebras - Lecture 2
Lie algebras are closely related to Lie groups , which are groups that are also smooth manifolds : any Lie group gives rise to a Lie algebra, which is its tangent space at the identity. Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to finite coverings Lie's third theorem.
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In mathematics, Lie group—Lie algebra correspondence allows one to study Lie groups, which are geometric objects, in terms of Lie algebras, which are linear objects. The purpose of the Elements of Mathematics by Nicolas Bourbaki is to provide a This volume concludes. Elements of Mathematics. Author : N. Author: Nicolas Bourbaki.
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