Results 11 to 20 of about 43,926 (156)

Yang-Baxter Systems, Algebra Factorizations and Braided Categories

Axioms, 2013
The Yang-Baxter equation first appeared in a paper by the Nobel laureate, C.N. Yang, and in R.J. Baxter’s work. Later, Vladimir Drinfeld, Vaughan F. R. Jones and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equation.
Florin F. Nichita
doaj   +1 more source

Limits of Quantum B-Algebras

Mathematics, 2021
Every set with a binary operation satisfying a true statement of propositional logic corresponds to a solution of the quantum Yang-Baxter equation. Quantum B-algebras and L-algebras are closely related to Yang-Baxter equation theory.
Aiping Gan, Aziz Muzammal, Yichuan Yang
doaj   +1 more source

Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups [PDF]

, 1997
The quantum dynamical Yang-Baxter (QDYB) equation is a useful generalization of the quantum Yang-Baxter (QYB) equation introduced by Gervais, Neveu, and Felder.
Etingof, Pavel, Varchenko, Alexander
core   +3 more sources

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.
A.P. Veselov, Adler, Baxter, Berenstein, Bourbaki, Buchstaber, Drinfeld, Etingof, Etingof, Fomin, Frenkel, Gaudin, Gohberg, Goncharenko, Goncharenko, Hietarinta, Hoffmann, Jimbo, Kulish, Moser, Noumi, Novikov, Odesskii, Reshetikhin, Reshetikhin, Suris, Takhtajan, Veselov, Veselov, Weinstein, Yang   +30 more
core   +2 more sources

Mathematics and Poetry · Yang–Baxter Equations, Boolean Algebras, and BCK-Algebras

Sci, 2022
The current paper explores the potential of the areas between mathematics and poetry. We will first recall some definitions and results that are needed to construct solutions of the Yang–Baxter equation.
Tugce Kalkan, Florin F. Nichita, Tahsin Oner, Ibrahim Senturk, Mehmet Terziler   +4 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation [PDF]

, 2005
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter equation.
Dancer, K. A., Isaac, P. S., Links, J.
core   +2 more sources

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
doaj   +1 more source