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Let $\mathcal{M}$ be a finite dimensional von Neumann algebra, then : $$\mathcal{M} \simeq \bigoplus_i M_{n_i}(\mathbb{C})$$

Question : Is it singly generated (as von Neumann algebra)? how ?

Allowed operations : $(A,B) \mapsto A+B$ or $A B$ and $A \mapsto \lambda A$ or $A + \lambda I$ or $\mathbf{A^*}$

Let $\mathcal{M}$ be a finite dimensional von Neumann algebra, then : $$\mathcal{M} \simeq \bigoplus_i M_{n_i}(\mathbb{C})$$

Question : Is it singly generated (as von Neumann algebra)? how ?

Allowed operations : $() \mapsto I$ , $(A) \mapsto \lambda A$ or $\mathbf{A^*}$ and $(A,B) \mapsto A+B$ or $A B$

Let $\mathcal{M}$ be a finite dimensional von Neumann algebra, then : $$\mathcal{M} \simeq \bigoplus_i M_{n_i}(\mathbb{C})$$

Question : Is it singly generated (as von Neumann algebra)? how ?

Allowed operations : $(A,B) \mapsto A+B$ , $(A,B) \mapsto A B$ , $A \mapsto \lambda A$ and $\mathbf{A \mapsto A^*}$

Let $\mathcal{M}$ be a finite dimensional von Neumann algebra, then : $$\mathcal{M} \simeq \bigoplus_i M_{n_i}(\mathbb{C})$$

Question : Is it singly generated (as von Neumann algebra)? how ?

Allowed operations : $(A,B) \mapsto A+B$ or $A B$ and $A \mapsto \lambda A$ or $A + \lambda I$ or $\mathbf{A^*}$

Let $\mathcal{A}$ be a finite dimensional von Neumann algebra, then : $$\mathcal{A} \simeq \bigoplus_i M_{n_i}(\mathbb{C})$$

Question : Is it singly generated (as von Neumann algebra)? how ?

Let $\mathcal{M}$ be a finite dimensional von Neumann algebra, then : $$\mathcal{M} \simeq \bigoplus_i M_{n_i}(\mathbb{C})$$

Question : Is it singly generated (as von Neumann algebra)? how ?

Allowed operations : $(A,B) \mapsto A+B$ , $(A,B) \mapsto A B$ , $A \mapsto \lambda A$ and $\mathbf{A \mapsto A^*}$