This is raw awesome.. what would this method be called?https://twitter.com/johncarlosbaez/status/1184539996994359296 …
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Yes, the groups O(2) and O(1,1) (2d rotation and Lorentz groups) both have Inonu-Wigner contractions to the 2d Galilei group, also called the "ax+b group". This can be seen using the algebras I'm talking about.
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Well, rather more than this is true, though. The intersection of the plane with the double-cone of which you speak is a level set of a quadratic form whose signature varies with the tilt of the plane. Its isometry group varies with the tilt, too: the tilt effects the contraction.
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