In R^2, a reflection can be achieved equally well by a rotation, because the group space of U(1) is connected. Visually I think of this as being able to peform a rotation that moves the positive y axis into the negative y axis and vice versa and without changing the x axis by imagining R^2 as embedded in R^3 and rotating about the x axis, so it is unchanged but the y axis sweeps through the extra dimension and eventually gets turned upside down.(adsbygoogle = window.adsbygoogle || []).push({});

In R^3, rotations and reflections are not connected. My question is, at what point does the analogue of the above reasoning fail for R^3, and also does the dis-connectedness of the group space have anything to do with the fact that the group is now non-abelian?

Thanks

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# Rotations and reflections

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