Results 11 to 20 of about 7,536,502 (162)
Introduction to the Yang-Baxter Equation with Open Problems
Axioms, 2012 The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C. N. Yang, and in statistical mechanics, in R. J. Baxter’s work.
Florin Nichita
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Yang-Baxter maps and integrable dynamics [PDF]
, 2002 The hierarchy of commuting maps related to a set-theoretical solution of the quantum Yang-Baxter equation (Yang-Baxter map) is introduced. They can be considered as dynamical analogues of the monodromy and/or transfer-matrices.
Alexander Veselov (1259028)
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Experimental realization of the Yang-Baxter Equation via NMR interferometry. [PDF]
Sci Rep, 2016 The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory.
Vind FA +6 more
europepmc +3 more sources
Yang-Baxter maps: dynamical point of view [PDF]
, 2006 A review of some recent results on the dynamical theory of the Yang- Baxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics.
Alexander Veselov (1259028)
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Abelian fixed point free endomorphisms and the Yang-Baxter equation [PDF]
, 2020 We obtain a simple family of solutions to the set-theoretic Yang-Baxter equation, one which depends only on considering special endomorphisms of a finite group.
Koch, Alan +2 more
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Yang-Baxter maps and the discrete KP hierarchy [PDF]
, 2009 We present a systematic construction of the discrete KP hierarchy in terms of Sato–Wilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with ...
Kakei, S., Willox, R., Nimmo, J.J.C.
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Rota-Baxter operators on the polynomial algebras, integration and averaging operators [PDF]
, 2014 The concept of a Rota–Baxter operator is an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota–Baxter operators and integrals in the case of the polynomial algebra k[x] k[x] .
Guo, Li +5 more
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On Solutions to the Set-Theoretical Yang-Baxter Equation in Wajsberg-Algebras
Axioms, 2018 In this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg algebras.
Tahsin Oner, Tugce Katican
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All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two
Complexity, 2020 Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation.
Duanmei Zhou, Jiawen Ding
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Problems on Skew Left Braces [PDF]
Advances in Group Theory and Applications, 2019 Braces were introduced by Rump as a generalization of Jacobson radical rings. It turns out that braces allow us to use ring-theoretic and group-theoretic methods for studying involutive solutions to the Yang–Baxter equation.
Leandro Vendramin
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