Are there real uses of abstract algebra in astrophysics?
There are certainly applications of number theory (as opposed to group theory/algebra - but you do also mention abstract mathematics in general) to astrophysics, though many would suggest these applications are on the boundary between real science and metaphysics.

One such application is the  measure problem - if we assume our universe is one of an infinite number of multiverses how can we draw conclusions about the fundamental physics of the many multiverses, for instance to say that intelligent life is possible in a given proportion.