Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation

DOI10.1007/s11005-022-01572-9OpenAlexW4290722538MaRDI QIDQ2674355

Bart Vlaar, Anastasia Doikou, Alexandros Ghionis

Publication date: 12 September 2022

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.03400

zbMATH Keywords

Drinfeld twistsset-theoretic Yang-Baxter equationquasi-bialgebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups (quantized function algebras) and their representations (20G42) Ring-theoretic aspects of quantum groups (16T20) Yang-Baxter equations (16T25)

Related Items (1)

Near braces and p$p$‐deformed braided groups

Cites Work

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• Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity
• Braces, radical rings, and the quatum Yang-Baxter equation.
• On quadrirational Yang-Baxter maps
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum R matrix for the generalized Toda system
• Yang-Baxter maps and integrable dynamics
• A characterization of finite multipermutation solutions of the Yang-Baxter equation
• A note on set-theoretic solutions of the Yang-Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation and new classes of \(\mathrm{R}\)-matrices
• A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups
• Classification of integrable equations on quad-graphs. The consistency approach
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation
• Skew braces as remnants of co-quasitriangular Hopf algebras in suplat
• Set-theoretic Yang-Baxter \& reflection equations and quantum group symmetries
• A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation
• Semi-braces and the Yang-Baxter equation
• On skew braces (with an appendix by N. Byott and L. Vendramin)
• Braces and the Yang-Baxter equation
• Skew braces and the Yang–Baxter equation
• On some unsolved problems in quantum group theory
• Permutation-type solutions to the Yang - Baxter and othern-simplex equations
• Yangians and classical Lie algebras
• Quasi-Hopf Algebras
• Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation
• Geometric Crystals and Set-Theoretical Solutions to the Quantum Yang-Baxter Equation
• On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation
• The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang–Baxter equation
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Set-theoretic Yang–Baxter equation, braces and Drinfeld twists

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