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YANG–BAXTER EQUATIONS IN QUANTUM INFORMATION
International Journal of Modern Physics B, 2012The connection between Yang–Baxter system and quantum information has been discussed. Based on the topological basis for both Temperley–Lieb (TL) algebra and Birman–Wenzl (BW) algebra the representations of N by N braiding matrices associated with the corresponding N2 by N2 ones are obtained.
Ge, Mo-Lin, Xue, Kang
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MAGNETIC MONOPOLES AND THE YANG-BAXTER EQUATIONS
International Journal of Modern Physics A, 1991A comparison is made between the new solutions of the Yang-Baxter equations, arising from curves of higher genus, and magnetic monopoles of higher charge. It is shown that essentially the same algebraic curves arise in both cases, and this leads to speculations about possibly more general solutions of the Yang-Baxter equations.
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2018
Let \(F\) be a linear space, \(R:F\otimes F\rightarrow F\otimes F\) an invertible linear map. It is well known that if \(R=S_{(12)}:f_1\otimes f_2 \mapsto f_2 \otimes f_1\), then one can define a representation of the symmetric group \({{\mathrm{S}}}_n\) on \(F^{\otimes n}\) by the following prescription: represent each element \(\sigma \in {{\mathrm{S}
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Let \(F\) be a linear space, \(R:F\otimes F\rightarrow F\otimes F\) an invertible linear map. It is well known that if \(R=S_{(12)}:f_1\otimes f_2 \mapsto f_2 \otimes f_1\), then one can define a representation of the symmetric group \({{\mathrm{S}}}_n\) on \(F^{\otimes n}\) by the following prescription: represent each element \(\sigma \in {{\mathrm{S}
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THE YANG-BAXTER EQUATION IN KNOT THEORY
International Journal of Modern Physics B, 1993The role played by the Yang-Baxter equation in generating knot invariants using the method of statistical mechanics is reexamined and elucidated. The formulation of knot invariants is made precise with the introduction of piecewise-linear lattices and enhanced vertex and interaction-round-a-face (IRF) models with strictly local weights.
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Hom-Yang-Baxter equations and Hom-Yang-Baxter systems
Communications in Algebra, 2023Shengxiang Wang, Shuangjian Guo
exaly
On the Johnson–Tzitzeica Theorem, Graph Theory, and Yang–Baxter Equations
Symmetry, 2021Florin F Nichita, Nichita Florin F
exaly
Two-component Yang–Baxter maps and star-triangle relations
Physica D: Nonlinear Phenomena, 2023Andrew P Kels
exaly
Folded and contracted solutions of coupled classical dynamical Yang–Baxter and reflection equations
Indagationes Mathematicae, 2021Jasper V Stokman
exaly