What Does the Second Index in SO(n,p) Represent?

[Aziza]

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.

 

[ShayanJ]

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

 

[dextercioby]

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.

 

[lpetrich]

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,
R^T.g.R = g