WebDec 15, 2024 · So what is the difference between the Yang--Baxter equation and the quantum Yang--Baxter equation? I guess that YBE came first and then came QYBE, but I don't see what is quantum about QYBE. What different properties do both have, and why should one consider them two versions of the same thing?
Yang–Baxter equation - Wikipedia
WebOct 23, 2024 · In physics, the Yang–Baxter equation (or star–triangle relation) is a consistency equation which was first introduced in the field of statistical mechanics. It … WebMar 23, 2024 · Consequently, post-Hopf algebras and relative Rota-Baxter operators give solutions of the Yang-Baxter equation in certain cocommutative Hopf algebras. Finally we characterize relative Rota-Baxter operators on Hopf algebras using relative Rota-Baxter operators on the Lie algebra of primitive elements, graphs and module bialgebra structures. mccormick livestock
All solutions of the Yang–Baxter-like matrix equation for rank-one ...
WebDec 1, 2012 · Many scientists have found solutions for the Yang-Baxter equation, obtaining qualitative results (using the axioms of various algebraic structures) or quantitative results (usually using... In physics, the Yang–Baxter equation (or star–triangle relation) is a consistency equation which was first introduced in the field of statistical mechanics. It depends on the idea that in some scattering situations, particles may preserve their momentum while changing their quantum internal states. It states that a matrix See more Let $${\displaystyle A}$$ be a unital associative algebra. In its most general form, the parameter-dependent Yang–Baxter equation is an equation for $${\displaystyle R(u,u')}$$, a parameter-dependent element … See more Let $${\displaystyle V}$$ be a module of $${\displaystyle A}$$, and $${\displaystyle P_{ij}=\phi _{ij}(P)}$$ . Let See more • Lie bialgebra • Yangian • Reidemeister move • Quasitriangular Hopf algebra See more A common ansatz for computing solutions is the difference property, $${\displaystyle R(u,u')=R(u-u')}$$ , where R depends only on a single … See more • "Yang-Baxter equation", Encyclopedia of Mathematics, EMS Press, 2001 [1994] See more WebApr 11, 2024 · Download a PDF of the paper titled Deformed solutions of the Yang-Baxter equation coming from dual weak braces and unital near-trusses, by Marzia Mazzotta and … mccormick loader joystick