Yang–Baxter endomorphisms

Conti R, Lechner G (2021)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2021


Book Volume: 103

Pages Range: 633-671

Journal Issue: 2

DOI: 10.1112/jlms.12387

Open Access Link: https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12387


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.

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Conti, R., & Lechner, G. (2021). Yang–Baxter endomorphisms. Journal of the London Mathematical Society-Second Series, 103(2), 633-671. https://dx.doi.org/10.1112/jlms.12387


Conti, Roberto, and Gandalf Lechner. "Yang–Baxter endomorphisms." Journal of the London Mathematical Society-Second Series 103.2 (2021): 633-671.

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