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Published in:
2020 | OriginalPaper | Chapter
7. Lie Groups
Author : Gerardo F. Torres del Castillo
Published in: Differentiable Manifolds
Publisher: Springer International Publishing
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Abstract
In many applications one encounters groups of transformations which contain one or several parameters, and on these groups we can define a structure of differentiable manifold. Two examples are the isometries of a Riemannian manifold and the symmetries of a second-order ODE, considered in Sects. 6.1 and 4.3, respectively. In this chapter we shall study these groups by themselves, combining their algebraic and differentiable structures. One of the main results of this combination is the fact that each of these groups has an associated Lie algebra which almost entirely determines the group.