Classification of unital extensions of AT-algebras

We prove that the six-term exact sequence in K-theory together with the Elliott invariants of the ideal and quotient is a complete invariant for certain unital extensions ofAT-algebras up to stable isomorphism. We also give some necessary and sufficient conditions for such extensions being AT-algebras or quasidiagonal extensions, and prove the above invariant with the equivalence class of unit is a complete invariant for unital quasidiagonal extensions of AT-algebras up to isomorphism.