Suris, Yuri B.; Veselov, Alexander P. Lax matrices for Yang-Baxter maps. (English) Zbl 1362.39016 J. Nonlinear Math. Phys. 10, Suppl. 2, 223-230 (2003). Summary: It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations on quad-graphs has been recently discovered by A. Bobenko and one of the authors, and by F. Nijhoff. Cited in 21 Documents MSC: 39A12 Discrete version of topics in analysis 16T25 Yang-Baxter equations 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics PDFBibTeX XMLCite \textit{Y. B. Suris} and \textit{A. P. Veselov}, J. Nonlinear Math. Phys. 10, 223--230 (2003; Zbl 1362.39016) Full Text: DOI References: [1] Drinfeld V.G.On some unsolved problems in quantum group theory.In ”Quantum groups” (Leningrad, 1990), Lecture Notes in Math., 1510, Springer, 1992, p. 1–8 [2] Goncharenko V.M. Veselov A.P.Yang-Baxter maps and matrix solitons.math-ph/0303032. To appear in Proceedings of NATO ARW conference (Cadiz, June 2002) [3] Etingof P.Geometric crystals and set-theoretical solutions to the quantum Yang-Baxter rela-tion.math.QA/0112278 · Zbl 1020.17008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.