Yang-Baxter Equations

TL;DR

This encyclopedia article provides an overview of Yang-Baxter equations, their mathematical significance, and their connections to electric networks and solvable models, serving as a comprehensive reference for researchers.

Contribution

It offers a detailed summary of Yang-Baxter equations, including an extended appendix on their relations to electric networks and solvable models, with historical context and references.

Findings

Connections between Yang-Baxter equations and electric networks

Applications to solvable models in physics

Historical overview of the equations' development

Abstract

Preprint of an Encyclopedia article (Encyclopedia of Mathematical Physics, eds. J.-P. Fran\c{c}oise, G.L. Naber and Tsou S.T., Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), volume 5, pages 465-473) extended with an appendix on relations of electric networks and solvable models. We welcome comments, especially on the added appendix. Please, note that the reference list has been restricted to only giving a few historical items and sources explicitly used. We apologize in advance for the many omissions.