Yang–Baxter endomorphisms

Every unitary solution of the Yang–Baxter equation (R-matrix) in dimension (Formula presented.) can be viewed as a unitary element of the Cuntz algebra (Formula presented.) and as such defines an endomorphism of (Formula presented.). These Yang–Baxter endomorphisms restrict and extend to several other (Formula presented.) - and von Neumann algebras, and furthermore define a II (Formula presented.) factor associated with an extremal character of the infinite braid group. This paper is devoted to a detailed study of such Yang–Baxter endomorphisms. We discuss the relative commutants of the subfactors induced by Yang–Baxter endomorphisms, a new perspective on algebraic operations on R-matrices such as tensor products and cabling powers, the characters of the infinite braid group defined by R-matrices, and ergodicity properties. This also yields new concrete information on partial traces and spectra of R-matrices.