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[tex]g_{j}(t)[/tex] be a curve in a group G, which goes through the identity element; g_j(t=0) = identity.

and:

[tex]\xi_{j}=\frac{d}{dt}g_{j}(t)\right|_{t=0}[/tex]

We know that:

[tex]\xi_{j}{\in}Lie(G)[/tex]

Why can we say:

1) [tex]hg(t)h^{-1}[/tex] (h is an element of the Group)

is also a curve in the group, which goes through the identity element, ie. g(t=0)=identity? [As an aside - how would you even go about doing this transformation - I mean if g(t) is a curve (for example g(t)=2t+4t^3), how can you combine this function with h and h^-1, which are, say, SU(2) matrices?]

2) [tex]g_{2}(t)\xi_{1}g_{2}(t)^{-1}{\in}Lie(G)[/tex]?

I mean, these look a bit like similarity transformations - can someone clarify why these statements are true?

Thanks.

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# Question on Lie Algebras

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