Maybe this is kind of a dumb question but... in a lot of places I see lie groups with names like SO(4,1) or O(1,3) or GL(2,3) referred to. I know what it means when you talk about, say, SO(n)-- that would be the rotation group in(adsbygoogle = window.adsbygoogle || []).push({}); ndimensions, or the special orthogonalnxnmatrices. But what does it mean when you add the comma and the second number? That seems to be a common notation, but I can't find a clear explanation of it.

Even more confusing, it seems like some people will nonchalantly swap the order of the two numbers, such that one source will be talking about SO(3,1) and another will be talking about SO(1,3) but they appear to really be talking about the same group! What does the transposition of the numbers mean?

(This wikipedia page describes in part a notation where you could have, for example, GL(3, R), where the ",R" provides a group that the matrix members are to be pulled from. But this is clearly not what is meant when the second number is an integer...!)

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# What is the difference between SO(3,1) and SO(1,3)?

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