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 $\mathbf{A^*}$