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PsychonautQQ
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Say H is a subgroup of topological group G. Let L_g: G--->G be denote a map of G acting on itself by a left translation of g. Show that L_g passes(descends) to the quotient G/H.
I am a bit confused here, for L_g to pass to the quotient G/H, it would have to be constant on the fibers of G/H. This means that if q: G--->G/H is the quotient map, then q(a)=q(b) implies that L_g(a) = L_g(b); I don't believe this implication is true. If q(a) = q(b) then ar = bs for some a,s in H. but if L_g(a) = L_g(b) this means that ag = bg.
Input anyone?
I am a bit confused here, for L_g to pass to the quotient G/H, it would have to be constant on the fibers of G/H. This means that if q: G--->G/H is the quotient map, then q(a)=q(b) implies that L_g(a) = L_g(b); I don't believe this implication is true. If q(a) = q(b) then ar = bs for some a,s in H. but if L_g(a) = L_g(b) this means that ag = bg.
Input anyone?
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