Introduction to the Theory of Compact Groups: Lectures, 1968-1969 (in 2 binders)Department of Mathematics, Tulane University, 1966 - Group theory |
Contents
Definition of a Lie Group | 10 |
LG as a Gmodule | 15 |
The Lie group property is a local property | 18 |
17 other sections not shown
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Common terms and phrases
abelian abelian group action addition adjoint assertion assume automorphism Banach Lie algebra Banach space called central Clearly closed subgroup commutative commutative diagram compact connected compact group compact Lie group connected group connected Lie group Consider contained covering defined definition direct discrete elements epic equivalent example exponential function extends fact function functor Further G₁ G₂ given H₁ Hence homeomorphism ideal identity injective invariant isomorphism L-module Lemma Let G Lie group G Lie subgroup locally monic Moreover morphism multiplication N₁ natural nbhd neighborhood norm normal subgroup Note obtain particular projective Proof Proposition quotient relative Remark respectively satisfying simple simply connected Split statements structure subgroup of G sufficiently small Suppose surjective theorem topological group totally disconnected unique vector space