Related papers: On Discrete 3-Dimensional Equations Associated wit…
Starting from the Kauffman-Lomonaco braiding matrix transforming the natural basis to Bell states, the spectral parameter describing the entanglement is introduced through Yang-Baxterization. It gives rise to a new type of solutions for…
We study a twisted version of the Yang-Baxter Equation, called the Hom-Yang-Baxter Equation (HYBE), which is motivated by Hom-Lie algebras. Three classes of solutions of the HYBE are constructed, one from Hom-Lie algebras and the others…
Tensor solutions ($r$-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the $R$-matrix solution of the quantum Yang-Baxter equation (QYBE), is an important structure appearing in…
We study geometric consistency relations between angles of 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…
This paper connects the quadrirational Yang-Baxter maps, which are two-dimensional integrable discrete systems of KdV type, and the elliptic Cremona system, which is a higher analogue of discrete Painlev\'e equations associated with…
We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced R-operators…
We find all solutions to the constant Yang--Baxter equation $R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}$ in three dimensions, subject to an additive charge-conservation ansatz. This ansatz is a generalisation of (strict) charge-conservation, for…
We propose a fully discrete analog of the massive Thirring model in light-cone coordinates by constructing its Lax-pair representation. This Lax-pair representation can also be used to define a new Yang-Baxter map, so we obtain a…
We study the root of unity limit of the lens elliptic gamma function solution of the star-triangle relation, for an integrable model with continuous and discrete spin variables. This limit involves taking an elliptic nome to a primitive…
We construct rational and piecewise-linear Yang-Baxter maps for a general N-reduction of the discrete BKP equation.
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not…
We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the…
Motivated by recent work on Hom-Lie algebras and the Hom-Yang-Baxter equation, we introduce a twisted generalization of the classical Yang-Baxter equation (CYBE), called the classical Hom-Yang-Baxter equation (CHYBE). We show how an…
This brief review surveys recent progress driven by the gauge/Yang-Baxter equation (YBE) correspondence. This connection has proven to be a powerful tool for discovering novel integrable lattice spin models in statistical mechanics by…
We resolve the `baxterization' problem with the help of the automorphism group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations. This infinite group of symmetries is realized as a non-linear (birational) Coxeter group…
We develop a categorical approach to the dynamical Yang-Baxter equation (DYBE) for arbitrary Hopf algebras. In particular, we introduce the notion of a dynamical extension of a monoidal category, which provides a natural environment for…
Superconformal indices of 3d N=2 supersymmetric field theories are investigated from the Yang-Baxter equation point of view. Solutions of the star-triangle relation, vertex and IRF Yang-Baxter equations are expressed in terms of the…
We obtain a new solution of the star-triangle relation with positive Boltzmann weights which contains as special cases all continuous and discrete spin solutions of this relation, that were previously known. This new master solution defines…
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are…
We explore the algebraic structure of a particular ansatz of Yang Baxter Equation which is inspired from the Bethe Ansatz treatment of the ASEP spin-model. Various classes of Hamiltonian density arriving from two types of R-Matrices are…