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This seems extraordinarily nitpicky. Like saying that unit complex numbers are technically not the group of plane rotations about a fixed point, but only isomor
by jacobolus 5y ago
This seems extraordinarily nitpicky. Like saying that unit complex numbers are technically not the group of plane rotations about a fixed point, but only isomorphic to it. Or for that matter like saying that the "real number line" is technically not a line, but only isomorphic to one.
- rnhmjoj 5y agoWell yeah, it is. The point I wanted to make is that these isomorphism are "exceptional"[1] and only hold for the lower dimensional groups. The general Spin group and quaterions are very different objects. [1]: https://en.wikipedia.org/wiki/Exceptional_isomorphism https://en.wikipedia.org/wiki/Exceptional_isomorphism