2020
DOI: 10.1112/jlms.12387
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Yang–Baxter endomorphisms

Abstract: Every unitary solution of the Yang-Baxter equation (R-matrix) in dimension d can be viewed as a unitary element of the Cuntz algebra O d and as such defines an endomorphism of O d. These Yang-Baxter endomorphisms restrict and extend to several other C *-and von Neumann algebras, and furthermore define a II1 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 in… Show more

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Cited by 2 publications
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“…To conclude, let us consider constant not necessarily involutive (but unitary) R-matrices in dimension 2. Strengthening a result of Dye [Dye03], it was recently shown that in dimension 2, every such R-matrix is type 1 equivalent (see p. 10) to one of the following four cases [CL19]:…”
mentioning
confidence: 90%
“…To conclude, let us consider constant not necessarily involutive (but unitary) R-matrices in dimension 2. Strengthening a result of Dye [Dye03], it was recently shown that in dimension 2, every such R-matrix is type 1 equivalent (see p. 10) to one of the following four cases [CL19]:…”
mentioning
confidence: 90%