This a reference request. We are writing a paper on calculi on AF algebras and their relation to Dirac operators. This is quite simple for UHF algebras (and we have references), but AF algebras introduce problems with the choice of a state (and so Hilbert space representation). I am sure that this is not new, thus the request.
To stress, we begin with the Bratteli diagram, not the AF algebra. Given isomorphisms of the matrix algebras, it is likely that possible states on the finite stages of the construction can be described in a relatively simple way. This is what we would like to look at, and to cite. We need a quite explicit description to make the states fit with the differential calculi.
We could proceed as it stands, working with states which are traces of matrices times a fixed diagonal matrix over every matrix summand, but we do not know how general this would be.
Apologies for not being well informed on this topic!
