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Unformatted text preview: X TG is a left invariant vector eld on G then * ( X ) is a right invariant vector eld whose value at e is-X ( e ). Further show that X 7 * ( X ) gives a Lie algebra isomorphism of the Lie algebra of left invariant vector elds with the Lie algebra of right invariant vector elds on G . (A Lie algebra isomorphism is a linear mapping A : V V which preserves the Lie bracket: A [ , ] = [ A,A ].) 4. MTA 5.2-1, parts (iii)(v): calculations on SO(3) 5. MTA 5.2-5: the Euclidean group...
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- Fall '08