Set-theoretical solutions of the Yang-Baxter and pentagon equations on semigroups

DOI10.1007/s00233-020-10100-xOpenAlexW3018466623MaRDI QIDQ2200883

Marzia Mazzotta, Paola Stefanelli, Francesco Catino

Publication date: 23 September 2020

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.05393

zbMATH Keywords

semigroupquantum Yang-Baxter equationpentagon equationset-theoretical solution

Mathematics Subject Classification ID

General structure theory for semigroups (20M10) Yang-Baxter equations (16T25)

Related Items (5)

Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces ⋮ Set-theoretic solutions of the Yang-Baxter equation associated to weak braces ⋮ Left non-degenerate set-theoretic solutions of the Yang–Baxter equation and dynamical extensions of q-cycle sets ⋮ Plactic monoids: a braided approach ⋮ Set-theoretic solutions of the pentagon equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
• Left semi-braces and solutions of the Yang-Baxter equation
• Zappa products
• Braces, radical rings, and the quatum Yang-Baxter equation.
• The interplay between \(k\)-graphs and the Yang-Baxter equation.
• Poisson Lie groups and pentagonal transformations
• Semigroups of \(I\)-type
• On pentagon, ten-term, and tetrahedron relations
• Pre-compatible almost endomorphisms and semigroups whose cube is a band.
• On the set-theoretical Yang-Baxter equation
• Braces and symmetric groups with special conditions
• 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
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation
• The matched product of the solutions to the Yang-Baxter equation of finite order
• Skew lattices and 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
• Quiver-theoretical approach to dynamical Yang-Baxter maps
• Skew braces and the Yang–Baxter equation
• On left quasinormal orthodox semigroups
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• On some unsolved problems in quantum group theory
• The hopf modules category and the hopf equation
• Transformations pentagonales
• A new family of set-theoretic solutions of the Yang–Baxter equation
• On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation
• Cohomology of idempotent braidings with applications to factorizable monoids
• Set-theoretical solutions of the pentagon equation on groups
• Dynamical extensions of quasi-linear left cycle sets and the Yang–Baxter equation
• Factorizable semigroups

This page was built for publication: Set-theoretical solutions of the Yang-Baxter and pentagon equations on semigroups