Yang–Baxter endomorphisms

Conti R, Lechner G (2021)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2021

Journal

Journal of the London Mathematical Society-Second Series London Mathematical Society

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

Abstract

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.

Authors with CRIS profile

Gandalf Lechner

Additional Organisation(s)

Lehrstuhl für Mathematik (Operatoralgebren)

Involved external institutions

Università degli studi "La Sapienza" IT Italy (IT) Cardiff University GB United Kingdom (GB)

How to cite

APA:

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

MLA:

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

BibTeX: Download