Abstract
In this chapter, we address structural aspects of Lie groups. Here an important issue is to see that for any closed normal subgroup N of a Lie group G, the quotient G/N carries a canonical Lie group structure, so that we may consider N and G/N as two pieces into which G decomposes. With this information, we then address the canonical factorization of a morphism of Lie groups into a surjective, a bijective, and an injective one. In particular, we describe some tools to calculate fundamental groups of Lie groups and homogeneous spaces.
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