SU(2) matrices act isometrically on the Riemann sphere with the chordal metric. At the same time the group of automorphisms of the Riemann sphere is isomorphic to the group SL(2, C) of isometries of(adsbygoogle = window.adsbygoogle || []).push({}); H 3(hyperbolic space) i.e. every orientation-preserving isometry ofH 3gives rise to a Möbius transformation on the Riemann sphere and viceversa.

Does this make SU(2) a normal(or even characteristic) subgroup of SL(2, C) when acting onH 3with the chordal metric in its conformal boundary(Riemann sphere) ?

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# SU(2) as a normal subgroup of SL(2, C)

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