Classification of unital extensions of -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 of A T -algebras up to stable isomorphism. We also give some necessary and sufficient conditions for such extensions being A T -algebras or quasidiagonal extensions, and prove the above invariant with the equivalence class of unit is a complete invariant for unital quasidiagonal extensions of A T -algebras up to isomorphism.