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Solutions of the Yang-Baxter equation

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Abstract

We give the basic definitions connected with the Yang-Baxter equation (factorization condition for a multiparticle S-matrix) and formulate the problem of classifying its solutions. We list the known methods of solution of the Y-B equation, and also various applications of this equation to the theory of completely integrable quantum and classical systems. A generalization of the Y-B equation to the case ofZ 2-graduation is obtained, a possible connection with the theory of representations is noted. The supplement contains about 20 explicit solutions.

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Authors
  1. P. P. Kulish
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  2. E. K. Sklyanin
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 95, pp. 129–160, 1980.

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Kulish, P.P., Sklyanin, E.K. Solutions of the Yang-Baxter equation. J Math Sci 19, 1596–1620 (1982). https://doi.org/10.1007/BF01091463

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