Related papers: Skew braces: a brief survey
Self-distributive (SD) structures form an important class of solutions to the Yang--Baxter equation, which underlie spectacular knot-theoretic applications of self-distributivity. It is less known that one go the other way round, and…
We have new solutions to the Yang-Baxter equation, from which we have constructed new link invariants containing more than two arbitrary parameters. This may be regarded as a generalization of the Jones' polynomial. We have also found…
The generalization of the the Yang-Baxter relation is proposed. In this generalization the spectral parameters of the particles change after the scattering. The corresponding algebraic structures are discussed. The corresponding action of…
Quivers over a fixed base set form a monoidal category with tensor product given by pullback. The quantum Yang-Baxter equation, or more properly the braid equation, is investigated in this setting. A solution of the braid equation in this…
We construct $R$-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They…
The (G, \theta)-Lie algebras are structures which unify the Lie algebras and Lie superalgebras. We use them to produce solutions for the quantum Yang-Baxter equation. The constant and the spectral-parameter Yang-Baxter equations and…
We consider the modified (or twisted) Yang-Baxter equations for the $SL_{q}(N)$ groups and $SL_{q}(N|M)$ supergroups. The general solutions for these equations are presented in the case of the linear quantum (super)groups. The introduction…
To the Yang-Baxter equation an additional relation can be added. This is the reflection equation which appears in various places, with or without spectral parameter. For example, in factorizable scattering on a half-line, integrable lattice…
In this short note, we construct some nontrivial examples of topological biquandle. The key ingredient of the construction is the notion of skew brace.
We study possible connections between Rota-Baxter operators of non-zero weight and non-skew-symmetric solutions of the classical Yang-Baxter equation on finite-dimensional quadratic Lie algebras. The particular attention is made to the case…
In this article, we study unitary rational solutions of the associative Yang-Baxter equation with three spectral parameters. We explain how such solutions arise from the geometry of vector bundles on a cuspidal cubic curve. Moreover, we…
The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra $s03_F$ is studied. The Baxterisation of the dual algebra is given in two different…
The theory of the parametric set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. The first step towards this objective is the introduction of certain generalizations of the familiar shelves and racks…
This work deals with an algebro-geometric theory of solutions of the classical Yang-Baxter equation based on torsion free coherent sheaves of Lie algebras on Weierstrass cubic curves.
We calculate the Roger-Yang skein algebra of the annulus with two interior punctures, $ \mathcal S^{RY}(\Sigma_{0, 2, 2})$, and show there is a surjective homomorphism from this algebra to the Kauffman bracket skein algebra of the closed…
Solutions to the twisted Yang-Baxter equation, arising from intertwiners for cyclic representations of $U_q(\widehat{sl}_n)$ are described via two coupled the lattice current algebras.
Semi-entwining structures are proposed as concepts simpler than entwining structures, yet they are shown to have interesting applications in constructing intertwining operators and braided algebras, lifting functors, finding solutions for…
It is shown that a Yang-Baxter system can be constructed from any entwining structure. It is also shown that, conversely, Yang-Baxter systems of certain type lead to entwining structures. Examples of Yang-Baxter systems associated to…
Set-theoretic solutions to the Yang-Baxter equation have been studied extensively by means of related algebraic systems such as cycle sets and braces, dynamical versions of which have also been developed. No work focuses on set-theoretic…
In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g.…