Related papers: A note on the eight tetrahedron equations
Yang-Baxter system related to quantum doubles is introduced and large class of both continuous and discrete symmetries of the solution manifold are determined. Strategy for solution of the system based on the symmetries is suggested and…
A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit…
The intertwiner of the quantized coordinate ring $A_q(sl_3)$ is known to yield a solution to the tetrahedron equation. By evaluating their $n$-fold composition with special boundary vectors we generate series of solutions to the Yang-Baxter…
Complete solution, more precisely, all invertible $4\times 4$ matrices $R,Q$ that solve Yang--Baxter system related to quantised braided groups, quantum doubles and other systems are given.
The Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2+1)-dimensional space-time. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The…
Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function r:X x X --> X x X which satisfies the braid relation. We…
We can recast the Yang-Baxter equation as a triple product equation. Assuming the triple product to satisfy some algebraic relations, we can find new solutions of the Yang-Baxter equation. This program has been completed here for the…
An integrable field theory, due to path-independence on the space-time plane, should yield together with an infinite set of independent conserved charges also similar dual charges determining the boundary and defect contributions. On the…
The Yang-Baxter equation plays a fundamental role in various areas of mathematics. Its solutions, called braidings, are built, among others, from Yetter-Drinfel'd modules over a Hopf algebra, from self-distributive structures, and from…
Computational methods are an important tool for solving the Yang-Baxter equations(in small dimensions), for classifying (unifying) structures, and for solving related problems. This paper is an account of some of the latest developments on…
We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions to the Yang-Baxter equation of small size. We show that there are 321931 involutive solutions of size nine, 4895272 involutive solutions of size ten…
A simple ansatz is proposed for two-color R-matrix satisfying the tetrahedron equation. It generalizes, on one hand, a particular case of the eight-vertex model to three dimensions, and on another hand - Hietarinta's permutation-type…
In this paper we study in detail the deformations introduced in [1] of the integrable structures of the AdS$_{2,3}$ integrable models. We do this by embedding the corresponding scattering matrices into the most general solutions of the…
We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model…
We consider involutive, non-degenerate, finite set theoretic solutions of the Yang-Baxter equation. Such solutions can be always obtained using certain algebraic structures that generalize nil potent rings called braces. Our main aim here…
We study scattering of three equal mass particles in one dimension. Integrable interactions are synonymous with non-diffractive scattering, meaning that the set of incoming momenta for any scattering event coincides with the set of outgoing…
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 study tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov tetrahedron equation, and Yang-Baxter maps, which are set-theoretical solutions to the quantum Yang-Baxter equation. In particular, we clarify the structure…
In this note we study `a la Baxter [1] the possible integrable manifolds of the asymmetric eight-vertex model. As expected they occur when the Boltzmann weights are either symmetric or satisfy the free-fermion condition but our analysis…
We propose a generic framework to obtain certain types of contracted and centrally extended algebras. This is based on the existence of quadratic algebras (reflection algebras and twisted Yangians), naturally arising in the context of…