LETTERS IN MATHEMATICAL PHYSICS, ISSN 0377-9017, 05/2020, Volume 110, Issue 5, pp. 885 - 909

Conformal classical Yang-Baxter equation and S-equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras...

Left-symmetric conformal algebra | ALGEBRAS | Conformal CYBE | Rota-Baxter operator | Conformal S-equation | O-operator | Lie conformal algebra | PHYSICS, MATHEMATICAL

Left-symmetric conformal algebra | ALGEBRAS | Conformal CYBE | Rota-Baxter operator | Conformal S-equation | O-operator | Lie conformal algebra | PHYSICS, MATHEMATICAL

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2017, Volume 86, Issue 307, pp. 2519 - 2534

Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation...

MATHEMATICS, APPLIED | SET-THEORETIC SOLUTIONS | CONJECTURE

MATHEMATICS, APPLIED | SET-THEORETIC SOLUTIONS | CONJECTURE

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2018, Volume 338, pp. 649 - 701

We involve simultaneously the theory of braided groups and the theory of braces to study set-theoretic solutions of the Yang–Baxter equation (YBE...

Yang–Baxter | Braces | Braided groups | QUADRATIC ALGEBRAS | HOPF-ALGEBRAS | EXTENSIONS | BICROSSPRODUCT | Yang-Baxter | MATHEMATICS | SKEW POLYNOMIAL-RINGS | SEMIGROUPS | MAPS | MATCHED PAIRS | HOMOLOGY | BINOMIAL RELATIONS | Algebra

Yang–Baxter | Braces | Braided groups | QUADRATIC ALGEBRAS | HOPF-ALGEBRAS | EXTENSIONS | BICROSSPRODUCT | Yang-Baxter | MATHEMATICS | SKEW POLYNOMIAL-RINGS | SEMIGROUPS | MAPS | MATCHED PAIRS | HOMOLOGY | BINOMIAL RELATIONS | Algebra

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 01/2018, Volume 17, Issue 1

In this work, we compute solutions of the Yang-Baxter associative equation in dimensions one and two...

Yang-Baxter equation | Frobenius algebra | Connes cocycle | dendriform algebra | D -equation | Associative algebra | D-equation | MATHEMATICS, APPLIED | HOPF-ALGEBRAS | MATHEMATICS | TREES | POISSON ALGEBRAS | HOMOLOGY | BIALGEBRAS

Yang-Baxter equation | Frobenius algebra | Connes cocycle | dendriform algebra | D -equation | Associative algebra | D-equation | MATHEMATICS, APPLIED | HOPF-ALGEBRAS | MATHEMATICS | TREES | POISSON ALGEBRAS | HOMOLOGY | BIALGEBRAS

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2019, Volume 52, Issue 35, p. 355201

.... It leads to a generalized operator star-triangle relation and a new solution of the Yang-Baxter equation written as an integral operator with a rarefied elliptic...

BETA-INTEGRALS | star-triangle relation | Yang-Baxter equation | MODELS | PHYSICS, MULTIDISCIPLINARY | Bailey lemma | PHYSICS, MATHEMATICAL | PARAMETER

BETA-INTEGRALS | star-triangle relation | Yang-Baxter equation | MODELS | PHYSICS, MULTIDISCIPLINARY | Bailey lemma | PHYSICS, MATHEMATICAL | PARAMETER

Journal Article

Applied surface science, ISSN 0169-4332, 2015, Volume 335, pp. 99 - 106

...–Baxter equation was also investigated for rough silica composite films.•Cassie–Baxter equation cannot be used for superhydrophobic surfaces...

Oleophobicity | Cassie–Baxter equation | Contact angle hysteresis | Superhydrophobicity | Work of adhesion | Cassie-Baxter equation | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | CONTACT-ANGLE HYSTERESIS | CHEMISTRY, PHYSICAL | HYDROPHOBICITY | SMOOTH | SURFACE-ROUGHNESS | DROPLETS | ADHESION | LENGTH SCALES | WORK | TRANSPARENT | MATERIALS SCIENCE, COATINGS & FILMS | WATER | Silica | Fluorine compounds | Copolymers | Perfluoroalkyls | Mathematical analysis | Particulate composites | Flats | Polymethyl methacrylates | Contact angle | Silicon dioxide

Oleophobicity | Cassie–Baxter equation | Contact angle hysteresis | Superhydrophobicity | Work of adhesion | Cassie-Baxter equation | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | CONTACT-ANGLE HYSTERESIS | CHEMISTRY, PHYSICAL | HYDROPHOBICITY | SMOOTH | SURFACE-ROUGHNESS | DROPLETS | ADHESION | LENGTH SCALES | WORK | TRANSPARENT | MATERIALS SCIENCE, COATINGS & FILMS | WATER | Silica | Fluorine compounds | Copolymers | Perfluoroalkyls | Mathematical analysis | Particulate composites | Flats | Polymethyl methacrylates | Contact angle | Silicon dioxide

Journal Article

Journal of algebra, ISSN 0021-8693, 2016, Volume 451, pp. 494 - 525

...–Baxter equation. For this, we provide two very different perspectives. On one hand, we show that the set of all set-theoretic solutions of the Yang...

Yang–Baxter equation | k-Graph | Set-theoretic solution | Yang-Baxter equation | K-Graph | SET-THEORETICAL SOLUTIONS | MATHEMATICS | SEMIGROUPS | BRACES | INVARIANTS | C-ASTERISK-ALGEBRAS | PRODUCT SYSTEMS | HIGHER-RANK GRAPHS | HOMOLOGY

Yang–Baxter equation | k-Graph | Set-theoretic solution | Yang-Baxter equation | K-Graph | SET-THEORETICAL SOLUTIONS | MATHEMATICS | SEMIGROUPS | BRACES | INVARIANTS | C-ASTERISK-ALGEBRAS | PRODUCT SYSTEMS | HIGHER-RANK GRAPHS | HOMOLOGY

Journal Article

Advances in colloid and interface science, ISSN 0001-8686, 2012, Volume 170, Issue 1-2, pp. 48 - 55

...–Baxter equations to interpret or predict contact angle data. We show that for surfaces wet with a composite interface, the commonly used form of the Cassie...

Cassie | Cassie–Baxter | Contact angle | Contact area | Rough surface | Contact line | Cassie-Baxter | SUPERHYDROPHOBIC SURFACES | TEMPERATURE-DEPENDENCE | WETTABILITY | SUPER-HYDROPHOBIC FILM | SOLID-SURFACES | WENZEL | CHEMISTRY, PHYSICAL | TEXTILE ASSEMBLIES | APPARENT CONTACT-ANGLE | FABRICATION | WATER DROPLET | Errors | Liquids | Penetration | Stability | Mathematical analysis | Pillars | Criteria

Cassie | Cassie–Baxter | Contact angle | Contact area | Rough surface | Contact line | Cassie-Baxter | SUPERHYDROPHOBIC SURFACES | TEMPERATURE-DEPENDENCE | WETTABILITY | SUPER-HYDROPHOBIC FILM | SOLID-SURFACES | WENZEL | CHEMISTRY, PHYSICAL | TEXTILE ASSEMBLIES | APPARENT CONTACT-ANGLE | FABRICATION | WATER DROPLET | Errors | Liquids | Penetration | Stability | Mathematical analysis | Pillars | Criteria

Journal Article

Journal of Algebra, ISSN 0021-8693, 10/2016, Volume 463, pp. 80 - 102

...–Baxter equation such that the associated permutation group G(X,r) is isomorphic, as a left brace, to B...

Yang–Baxter equation | Brace | Set-theoretic solution | MATHEMATICS | SET-THEORETIC SOLUTIONS | Yang Baxter equation

Yang–Baxter equation | Brace | Set-theoretic solution | MATHEMATICS | SET-THEORETIC SOLUTIONS | Yang Baxter equation

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2019, Volume 517, pp. 1 - 18

...–Drinfeld space M of quasi-triangular solutions to the classical Yang–Baxter equation. In this setting M is a finite disjoint union of components; exactly ϕ(n...

Frobenius functionals | Cremmer–Gervais r-matrices | Parabolic subalgebras | Classical Yang–Baxter equation | Principal elements | Frobenius Lie algebras | LIE-ALGEBRAS | MATHEMATICS | Classical Yang-Baxter equation | INDEX | Cremmer-Gervais r-matrices | Subprime loans | Algebra

Frobenius functionals | Cremmer–Gervais r-matrices | Parabolic subalgebras | Classical Yang–Baxter equation | Principal elements | Frobenius Lie algebras | LIE-ALGEBRAS | MATHEMATICS | Classical Yang-Baxter equation | INDEX | Cremmer-Gervais r-matrices | Subprime loans | Algebra

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 7/2016, Volume 345, Issue 2, pp. 507 - 543

...–Baxter equation with a rank 1 symmetry algebra. The reduced R-operators reproduce at their bottom the standard...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | VERTEX-FACE CORRESPONDENCE | BETA-INTEGRALS | MATRIX | FUSION | SYMMETRY | INTEGRABLE QUANTUM-SYSTEMS | MODELS | IDENTITIES | 6J-SYMBOLS | PHYSICS, MATHEMATICAL | OPERATORS | Algebra

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | VERTEX-FACE CORRESPONDENCE | BETA-INTEGRALS | MATRIX | FUSION | SYMMETRY | INTEGRABLE QUANTUM-SYSTEMS | MODELS | IDENTITIES | 6J-SYMBOLS | PHYSICS, MATHEMATICAL | OPERATORS | Algebra

Journal Article

12.
Full Text
Retractability of solutions to the Yang–Baxter equation and p-nilpotency of skew braces

International Journal of Algebra and Computation, ISSN 0218-1967, 02/2020, Volume 30, Issue 1, pp. 91 - 115

...–Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups...

Bieberbach group | MATHEMATICS | Yang-Baxter equation | MULTIPERMUTATION SOLUTIONS | set-theoretic solution | multipermutation solution | skew brace | PRODUCT | RINGS | SET-THEORETIC SOLUTIONS | unique product property

Bieberbach group | MATHEMATICS | Yang-Baxter equation | MULTIPERMUTATION SOLUTIONS | set-theoretic solution | multipermutation solution | skew brace | PRODUCT | RINGS | SET-THEORETIC SOLUTIONS | unique product property

Journal Article

Advances in Mathematics, ISSN 0001-8708, 02/2019, Volume 343, pp. 273 - 315

We show that all strongly non-degenerate trigonometric solutions of the associative Yang–Baxter equation (AYBE...

Associative Yang–Baxter equation | Fukaya category | Square-tiled surface | MATHEMATICS | Associative Yang-Baxter equation | GENUS | TRIGONOMETRIC SOLUTIONS | CURVES | MIRROR SYMMETRY

Associative Yang–Baxter equation | Fukaya category | Square-tiled surface | MATHEMATICS | Associative Yang-Baxter equation | GENUS | TRIGONOMETRIC SOLUTIONS | CURVES | MIRROR SYMMETRY

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2016, Volume 49, Issue 39, p. 395202

.... First, we prove that for relativistic (and non-relativistic) tops, such Lax pairs with spectral parameters follow from the associative Yang-Baxter equation and its degenerations...

noncommutative integrable systems | elliptic integrable systems | Painlevé VI equation | Euler-Arnold tops | YANG-BAXTER EQUATION | QUADRATIC ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | LIE | CALOGERO-MOSER SYSTEMS | MODEL | PHYSICS, MATHEMATICAL | SYMMETRY | Painleve VI equation | PAIRS

noncommutative integrable systems | elliptic integrable systems | Painlevé VI equation | Euler-Arnold tops | YANG-BAXTER EQUATION | QUADRATIC ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | LIE | CALOGERO-MOSER SYSTEMS | MODEL | PHYSICS, MATHEMATICAL | SYMMETRY | Painleve VI equation | PAIRS

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2019, Volume 52, Issue 48, p. 485201

We construct birational maps that satisfy the parametric set-theoretical Yang?Baxter equation and its entwining generalisation...

Darboux transformations | NLS type equations | YANG-BAXTER MAPS | PHYSICS, MULTIDISCIPLINARY | entwining parametric Yang?Baxter maps | PHYSICS, MATHEMATICAL | Liouville integrability

Darboux transformations | NLS type equations | YANG-BAXTER MAPS | PHYSICS, MULTIDISCIPLINARY | entwining parametric Yang?Baxter maps | PHYSICS, MATHEMATICAL | Liouville integrability

Journal Article

Journal of Algebra, ISSN 0021-8693, 05/2020, Volume 549, pp. 268 - 290

We use ring-theoretic methods and methods from the theory of skew braces to produce set-theoretic solutions to the reflection equation...

Yang-Baxter equation | Radical ring | Brace | Reflection equation | Skew brace | MATHEMATICS | MULTIPERMUTATION SOLUTIONS | MAPS | SKEW BRACES | SET-THEORETIC SOLUTIONS

Yang-Baxter equation | Radical ring | Brace | Reflection equation | Skew brace | MATHEMATICS | MULTIPERMUTATION SOLUTIONS | MAPS | SKEW BRACES | SET-THEORETIC SOLUTIONS

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2019, Volume 52, Issue 22, p. 225401

We show how so-called Yang-Baxter (YB) deformations of sigma models, based on an R-matrix solving the classical Yang-Baxter equation (CYBE...

ADS | marginal deformations | SYMMETRIES | ETA | PHYSICS, MULTIDISCIPLINARY | Wess-Zumino-Witten model | classical Yang-Baxter equation | PHYSICS, MATHEMATICAL | T-DUALITY | STRING THEORY | string on AdS | Physics - High Energy Physics - Theory

ADS | marginal deformations | SYMMETRIES | ETA | PHYSICS, MULTIDISCIPLINARY | Wess-Zumino-Witten model | classical Yang-Baxter equation | PHYSICS, MATHEMATICAL | T-DUALITY | STRING THEORY | string on AdS | Physics - High Energy Physics - Theory

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2019, Volume 372, Issue 10, pp. 7191 - 7223

For a finite involutive non-degenerate solution (X,r) of the Yang-Baxter equation it is known that the structure monoid M(X,r...

MATHEMATICS | Yang-Baxter equation | COHOMOLOGY | set-theoretic solution | EXTENSIONS | RINGS | SEMI-BRACES | (skew) brace | prime ideal | QUADRATIC MONOMIAL RELATIONS

MATHEMATICS | Yang-Baxter equation | COHOMOLOGY | set-theoretic solution | EXTENSIONS | RINGS | SEMI-BRACES | (skew) brace | prime ideal | QUADRATIC MONOMIAL RELATIONS

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 10/2016, Volume 189, Issue 1, pp. 1472 - 1485

We survey the matrix product solutions of the Yang–Baxter equation recently obtained from the tetrahedron equation...

Yang–Baxter map | tetrahedron equation | generalized quantum group | Yang–Baxter equation | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics | CRYSTAL BASES | Yang-Baxter equation | ANALOG | PHYSICS, MULTIDISCIPLINARY | Yang-Baxter map | VERTEX MODELS | PHYSICS, MATHEMATICAL

Yang–Baxter map | tetrahedron equation | generalized quantum group | Yang–Baxter equation | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics | CRYSTAL BASES | Yang-Baxter equation | ANALOG | PHYSICS, MULTIDISCIPLINARY | Yang-Baxter map | VERTEX MODELS | PHYSICS, MATHEMATICAL

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 109, Issue 4, pp. 843 - 856

We introduce the notion of N-reflection equation which provides a generalization of the usual classical reflection equation describing integrable boundary conditions...

Geometry | Classical reflection equation | 17B63 | Theoretical, Mathematical and Computational Physics | Complex Systems | Non-skew-symmetric r -matrices | Group Theory and Generalizations | Classical Yang–Baxter equation | Gaudin models | Physics | 37K10 | Non-skew-symmetric r-matrices | INTEGRABLE MODELS | BOUNDARY-CONDITIONS | Classical Yang-Baxter equation | HAMILTONIAN STRUCTURES | PHYSICS, MATHEMATICAL | R-MATRICES | Analysis | Models | Algebra | Mathematics | Nonlinear Sciences | Exactly Solvable and Integrable Systems | Mathematical Physics

Geometry | Classical reflection equation | 17B63 | Theoretical, Mathematical and Computational Physics | Complex Systems | Non-skew-symmetric r -matrices | Group Theory and Generalizations | Classical Yang–Baxter equation | Gaudin models | Physics | 37K10 | Non-skew-symmetric r-matrices | INTEGRABLE MODELS | BOUNDARY-CONDITIONS | Classical Yang-Baxter equation | HAMILTONIAN STRUCTURES | PHYSICS, MATHEMATICAL | R-MATRICES | Analysis | Models | Algebra | Mathematics | Nonlinear Sciences | Exactly Solvable and Integrable Systems | Mathematical Physics

Journal Article