# State spaces of AF algebras using Bratteli diagrams

AF algebras can be constructed from matrix algebras by using Bratteli diagrams. By Choi's theorem the pure state space of a matrix algebra is a complex projective space. I am assuming that someone has put these together and given the state space of an AF algebra as a limit (using the Bratteli diagram) of finite dimensional manifolds. I would be very grateful if someone could point me in the right direction to read about this.

This is a specialisation to AF algebras of a question I asked earlier which received 8 upvotes but no comments. I have tried to make it more specific.

• Just to clarify, the state space will be an inverse limit of the finite dimensional ones (the AF algebra is the closure of the algebraic direct limit of finite dimensional semisimple AF algebras). – David Handelman Jun 7 at 13:03