I have two mapping tori $A_{n}$={$f\in C([0,1], M_{n}(\mathbb{R}))\mid f(1)=\alpha_{1}(f(0))$}, $B_{n}$={$f\in C([0,1], M_{n}(\mathbb{R}))\mid f(1)=\alpha_{2}(f(0))$} where $\alpha_{1}, \alpha_{2}$ are two inner automorphisms of $M_{n}(\mathbb{R})$. I need to pick the connecting maps in the inductive sequence such that the limit algebras become non-isomorphic. Any suggestions? 

I already constructed some connecting maps that produce simple algebras with isomorphic $K_{0}$-groups. If I know how to produce non-isomorphic limit algebras, I can modify my connecting maps accordingly.