On the von Neumann algebras associated to Yang–Baxter operators

Bożejko and Speicher associated a finite von Neumann algebra MT to a self-adjoint operator T on a complex Hilbert space of the form H⊗ H which satisfies the Yang–Baxter relation and \| T \| < 1 . We show that if dim (H) ⩾ 2, then MT is a factor when T admits an eigenvector of some special form.