Bozejko 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 somespecial form. © 2020 The Author(s). Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.