The authors complete the classification of all 4×4 solutions of the quantum Yang-Baxter equation, including non-regular cases, and examine their relation to Lax operators.
Yang-Baxter Equations
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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.
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All 4 x 4 solutions of the quantum Yang-Baxter equation
The authors complete the classification of all 4×4 solutions of the quantum Yang-Baxter equation, including non-regular cases, and examine their relation to Lax operators.