I have two vertex operator algebras and I would like to show that *as graded vector spaces*, they are isomorphic, rather than as algebras.

The issue is I have not found anything in the literature that has done this for a particular case. One idea I had was since there is a cohomology theory for VOAs, there are tools to compare invariants of them as algebras, and I am hoping there may be something in the literature which uses this (or some other method), to make a statement about them as graded vector spaces.

I would highly appreciate if anyone can point me to a paper that develops any of these ideas, that is, if one can 'descend' a statement of two VOAs to something about them as graded vector spaces.