Euclidian and Hyperbolic rotations

neerajareen
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Do hyperbolic rotations of euclidian space and ordinary rotations of euclidian space form a group?
 
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Yes, the ordinary rotations form a group called ##SO(n)##. The hyperbolic rotations also form a group, that's apparently called ##SO^+(1,1)##.
 
No I meant, can they form a group together. Can they be put in the same group? Just like how Lorentz boosts and rotations are combined into the Lorentz group?
 
The world of 2\times 2 complex matrices is very colorful. They form a Banach-algebra, they act on spinors, they contain the quaternions, SU(2), su(2), SL(2,\mathbb C), sl(2,\mathbb C). Furthermore, with the determinant as Euclidean or pseudo-Euclidean norm, isu(2) is a 3-dimensional Euclidean space, \mathbb RI\oplus isu(2) is a Minkowski space with signature (1,3), i\mathbb RI\oplus su(2) is a Minkowski space with signature (3,1), SU(2) is the double cover of SO(3), sl(2,\mathbb C) is the...

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