Dg2test4 - Differential Geometry 2 Test 4(1 Let G be a connected Lie group with Lie algebra g let K ⊂ G be a connected Lie subgroup and k ⊂ g

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Unformatted text preview: Differential Geometry 2 Test 4 (1) Let G be a connected Lie group with Lie algebra g; let K ⊂ G be a connected Lie subgroup and k ⊂ g its Lie algebra. Prove that if k is an ideal in g then K is normal in G. (The converse is true without connectedness.) (2) Let G be the matrix Lie group comprising all matrices of the form ax 01 with 0 < a ∈ R x. Prove that G is not isomorphic to the direct product of two connected one-dimensional Lie groups. 1 ...
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This note was uploaded on 07/08/2011 for the course MTG 6256 taught by Professor Robinson during the Spring '09 term at University of Florida.

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