Is Abstract Algebra useful in theoretical Relativity and/or Cosmology? If so can anyone give me some examples or point me towards a good book with that emphasis if it is one?
Thanks in advance.
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Modern Algebra is used quite a bit in Quantum Field Theory to represent the Lorentz Group.
Since successive boosts can be performed in one boost, we can see that a boost applied to boost is a boost, implying that Lorentz Boosts form a group. You then use some representation theory to represent those boosts as matrices with some basis, and you can apply these to fields to boost them into different reference frames.
For relativity and cosmology, it's mostly differential geometry you'll need, but as vector spaces are also groups, I suppose you could say Modern Algebra is involved there.