Titlebook: Structure and Geometry of Lie Groups; Joachim Hilgert,Karl-Hermann Neeb Book 2012 Springer Science+Business Media, LLC 2012 Lie algebras.L

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Elementary Structure Theory of Lie Algebrasras of matrices, and we shall also see in Chapter?. below how to associate a Lie algebra to any Lie group. This correspondence is the guiding motivation behind the theory of finite-dimensional Lie algebras to which we now turn in some depth.

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Representation Theory of Lie Algebrasly plays an important role in structural questions. In this chapter, we first introduce the universal enveloping algebra . of a Lie algebra .. This is a unital associative algebra containing . as a Lie subalgebra and is generated by .. It has the universal property that each representation of . exte

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Basic Lie Theorys (multiplication and inversion) are smooth. Here we use vector fields to build the key tools of Lie theory. The Lie functor which associates a Lie algebra with a Lie group and the exponential function from the Lie algebra to the Lie group. They provide the means to translate global problems into in

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Smooth Actions of Lie Groupsomorphic automorphisms of complex domains, or groups of canonical transformations in hamiltonian mechanics. In all these cases, one considers group actions on manifolds by smooth maps. Even though the focus of this book is the geometry and structure theory of Lie groups rather than their application

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