Yang–Baxter endomorphisms
Every unitary solution of the Yang–Baxter equation (R‐matrix) in dimension d can be viewed as a unitary element of the Cuntz algebra Od and as such defines an endomorphism of Od . These Yang–Baxter endomorphisms restrict and extend to several other C∗ ‐ and von Neumann algebras, and furthermore define a II 1 factor associated with an extremal character of the infinite braid group. This paper is devoted to a detailed study of such Yang–Baxter endomorphisms.