The Structure of Lie Groups |
Contents
Topological Groups | 1 |
Compact Groups | 14 |
Elementary Structure Theory | 33 |
Copyright | |
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Common terms and phrases
abelian adjoint representation analytic homomorphism analytic manifold isomorphism analytic map analytic subgroup analytic tangent vector belongs canonical map Cartan subalgebra Chapter clear closed in G closed subgroup commutator compact group compact subgroup completes the proof complex analytic group complex analytic representation connected component contains continuous homomorphism defined denote direct sum element of G endomorphism evidently finite follows G-module G₁ group G Haar integral Hence identity map induces injective integer kernel Lemma Let f Let G Let H Lie algebra homomorphism Lie group linear endomorphism locally compact morphism nilpotent non-trivial normal subgroup open connected neighborhood open set positive real number power series power series function power series map proof of Theorem Proposition 3.1 proved representation of G restriction semidirect product sequence simply connected structure subalgebra subgroup of G subset subspace suppose Theorem 3.1 topological group toroid unipotent V₁ vector group vector space whence