Normal Subgroups, Nilpotent and Solvable Lie Groups
Part of the
Springer Monographs in Mathematics
book series (SMM)
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.
KeywordsNormal Subgroup Fundamental Group Semidirect Product Canonical Factorization Universal Covering Group
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Bourbaki, N., “Lie Groups and Lie Algebras, Chap. 1–3”, Springer, Berlin, 1989
Hochschild, G., “The Structure of Lie Groups, ” Holden Day, San Francisco, 1965
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