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Quick Question: SO(n) vs SO(n,1) ?

  1. Dec 5, 2014 #1
    I know that SO(n) means a rotation in n dimensions, but sometimes I see a second index, such as SO(n,p). What does p mean? I cannot find much resources on this.
  2. jcsd
  3. Dec 6, 2014 #2


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    The special case SO(3,1)(or SO(1,3)) is called Lorentz group. I think its generalization obvious.
  4. Dec 6, 2014 #3


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    O(n,1) is the Lorentz group in n space dimensions. O(n,2) is the conformal group in n space dimensions. There are no special names for p>2.
  5. Dec 20, 2014 #4
    The group SO(m,n) is the group of rotations that keep invariant a symmetric metric with signature m + signs and n - signs. The signature is the signs of its eigenvalues. So SO(m,n) is closely related to SO(m+n). Symbolically, for R in SO(m,n) and metric g,
    RT.g.R = g
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