This preview shows page 1. Sign up to view the full content.
This is the end of the preview. Sign up
to
access the rest of the document.
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 onedimensional Lie groups. 1 ...
View
Full
Document
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.
 Spring '09
 Robinson

Click to edit the document details