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Aaron Tikuisis
Aaron Tikuisis
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David
David
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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. Then, I can modify my connecting maps accordingly.

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. Then, I can modify my connecting maps accordingly.

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.

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David
David
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Inductive limit of mapping tori

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. Then, I can modify my connecting maps accordingly.