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 $\mathbf{A \mapsto A^*}$