Unformatted text preview: X ⊂ TG is a left invariant vector ﬁeld on G then φ * ( X ) is a right invariant vector ﬁeld whose value at e is-X ( e ). Further show that X 7→ φ * ( X ) gives a Lie algebra isomorphism of the Lie algebra of left invariant vector ﬁelds with the Lie algebra of right invariant vector ﬁelds on G . (A Lie algebra isomorphism is a linear mapping A : V → V which preserves the Lie bracket: A [ ξ,η ] = [ Aξ,Aη ].) 4. MTA 5.2-1, parts (iii)–(v): calculations on SO(3) 5. MTA 5.2-5: the Euclidean group...
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This note was uploaded on 01/04/2012 for the course CDS 202 taught by Professor Marsden,j during the Fall '08 term at Caltech.
- Fall '08