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Yang–Baxter Equations, Computational Methods and Applications [PDF]

Axioms, 2015
Computational methods are an important tool for solving the Yang–Baxter equations (in small dimensions), for classifying (unifying) structures and for solving related problems.
Florin F. Nichita
doaj   +5 more sources

Classical Yang-Baxter equation from β-supergravity [PDF]

Journal of High Energy Physics, 2019
Yang-Baxter deformations of superstring σ-models have recently inspired a supergravity solution generating technique. Using the open/closed string map and a Killing bi-vector as a deformation parameter, new solutions can be built, such that the ...
Ilya Bakhmatov, Edvard T. Musaev
doaj   +6 more sources

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, Foerster A, Oliveira IS, Sarthour RS, Soares-Pinto DO, Souza AM, Roditi I.   +6 more
europepmc   +4 more sources

Generalized Yang-Baxter Equation [PDF]

Modern Physics Letters A, 1993
A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative.
Kashaev, R. M., Stroganov, Yu. G.
core   +5 more sources

Quantum groups, Yang–Baxter maps and quasi-determinants

Nuclear Physics B, 2018
For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang–Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum ...
Zengo Tsuboi
doaj   +6 more sources

Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems

Journal of High Energy Physics, 2018
The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations.
R. S. Vieira
doaj   +4 more sources

Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation [PDF]

Heliyon
This article explores the application of exact line search and successive over-relaxation techniques to enhance the convergence of Newton method in solving the Yang-Baxter matrix equation for nontrivial numerical solutions. Moreover, the normwise, mixed,
Chacha Stephen Chacha
europepmc   +2 more sources

On the Colored and the Set-Theoretical Yang–Baxter Equations

Axioms, 2021
This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation.
Laszlo Barna Iantovics, Florin Felix Nichita   +1 more
doaj   +1 more source

Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems

Axioms, 2023
This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, E I π+U=O.
Florin F. Nichita
doaj   +1 more source

Solutions of Yang–Baxter Equation of Mock-Lie Algebras and Related Rota Baxter Algebras

Computer Sciences & Mathematics Forum, 2023
This paper discusses the relationship between Mock-Lie algebras, Lie algebras, and Jordan algebras. It highlights the importance of the Yang–Baxter equation and symplectic forms in the study of integrable systems, quantum groups, and topological quantum ...
Amir Baklouti
doaj   +1 more source