Quasi-linear Cycle Sets and the Retraction Problem for Set-theoretic Solutions of the Quantum Yang-Baxter Equation

DOI10.1142/S1005386716000183zbMath1335.81095MaRDI QIDQ2796973

Wolfgang Rump

Publication date: 30 March 2016

Published in: Algebra Colloquium (Search for Journal in Brave)

zbMATH Keywords

quantum Yang-Baxter equationcycle setset-theoretical solution

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Finite abelian groups (20K01) Representations of groups as automorphism groups of algebraic systems (20F29) Jacobson radical, quasimultiplication (16N20) Subgroups of symmetric groups (20B35) Yang-Baxter equations (16T25)

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Cites Work

• Monoids and groups of I-type.
• Braces, radical rings, and the quatum Yang-Baxter equation.
• Classification of cyclic braces.
• Retractability of set theoretic solutions of the Yang-Baxter equation
• Skew polynomial rings with binomial relations
• Classical solutions of the quantum Yang-Baxter equation
• Binomial semigroups
• Semigroups of \(I\)-type
• Yang-Baxter maps and integrable dynamics
• On the set-theoretical Yang-Baxter equation
• A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
• Homological properties of Sklyanin algebras
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Geometric Crystals and Set-Theoretical Solutions to the Quantum Yang-Baxter Equation
• A combinatorial approach to the set-theoretic solutions of the Yang–Baxter equation
• Indecomposable set-theoretical solutions to the quantum Yang-Baxter equation on a set with a prime number of elements