Results 11 to 20 of about 44,436 (212)
Stochasticization of Solutions to the Yang–Baxter Equation [PDF]
Annales Henri Poincaré, 2019 51 pages, 19 ...
Aggarwal, Amol +2 more
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Skew braces and the Yang–Baxter equation [PDF]
Mathematics of Computation, 2016 Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation. We generalize Rump’s braces to the non-commutative setting and use this new structure to study not necessarily involutive non-degenerate set-theoretical solutions of the Yang–Baxter equation.
L. Guarnieri, Leandro Vendramin
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Multipermutation Solutions of the Yang–Baxter Equation [PDF]
Communications in Mathematical Physics, 2011 Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function r:X x X --> X x X which satisfies the braid relation. We examine solutions here mainly from the point of view of finite permutation groups: a solution gives rise to a map ...
Gateva-Ivanova, Tatiana, Cameron, Peter
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Classical Yang-Baxter equation from β-supergravity
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
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Semi-braces and the Yang–Baxter equation
Journal of Algebra, 2017 A brace is a set \(B\) together with two binary operations \(+\) and \(\circ\) such that \((B,+)\) is an abelian group, \((B,\circ)\) is a group, and \[ a\circ (b+c)= a\circ b - a +a \circ c, \] for all \(a,b,c\in B\). The importance of this algebraic structure is that a brace produces a set-theoretic solution of the Yang-Baxter equation, and, by ...
Catino, Francesco +2 more
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Yang-Baxter Maps from the Discrete BKP Equation
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We construct rational and piecewise-linear Yang-Baxter maps for a general N-reduction of the discrete BKP equation.
Saburo Kakei +2 more
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Yang-Baxter equation and cryptography
, 2022 We find a method to construct iteratively from a non-degenerate involutive set-theoretic solution of the Yang-Baxter equation an infinite family of very large non-degenerate involutive set-theoretic solutions. In case the initial solution is irretractable, all the induced solutions are also irretractable. In case the initial solution is indecomposable,
Chouraqui, Fabienne
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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 +2 more sources
GENERALIZED YANG-BAXTER EQUATION [PDF]
Modern Physics Letters A, 1993 A generalization of the Yang-Baxter equation is proposed. It enables us to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit solutions to the generalized equations are found. They are related with Boltzmann weights of the sl (3) chiral Potts
Kashaev, R. M., Stroganov, Yu. G.
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Braces and the Yang–Baxter Equation [PDF]
Communications in Mathematical Physics, 2014 Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation are discussed and many consequences are derived. In particular, for each positive integer $n$ a finite square-free multipermutation solution of the Yang-Baxter equation with multipermutation level $n$ and an abelian involutive ...
Jespers, Eric, Cedo, F., Okninski, J.
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