Are there real uses of abstract algebra in astrophysics? It is known that a physicist must have, at least in general, a good level in mathematics in order to research and understand other people's works. Linear algebra is a good example, as ODEs and calculus.

I suppose that some astrophysicists have deep knowledge of abstract mathematics and there are some applications of it (for example, I've been told that there is a connection between topology and cosmology). I wondered if there are some field in Astrophysics in which abstract algebra (i.e. fields, rings, category theory...) has been applied.
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.