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I've added the allowed operation with the identity.
Sebastien Palcoux
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Are the finite dimensional von Neumann algebras, singly generated?

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 $\mathbf{A^*}$

Sebastien Palcoux
  • 27k
  • 5
  • 74
  • 186