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Published in:
2016 | OriginalPaper | Chapter
6. Lie Groups
Author : Torsten Wedhorn
Published in: Manifolds, Sheaves, and Cohomology
Publisher: Springer Fachmedien Wiesbaden
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Abstract
A Lie group is a premanifold together with a group structure such that multiplication and inversion are morphisms of premanifolds. They play an important role as symmetry groups of premanifolds and this is also the main focus of this chapter. Hence after defining Lie groups and Lie subgroups and studying their topology we will consider Lie groups acting on premanifolds in Sect. 6.2. The main result is the existence of quotients of premanifolds by a proper and free Lie group action in the last section.