相关论文: Stochasticization of Solutions to the Yang-Baxter …
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is to replace the single multiplication on a left near-ring…
Employing the algebraic structure of the left brace and the dynamical extensions of cycle sets, we investigate a class of indecomposable involutive set-theoretic solutions of the Yang-Baxter equation having specific imprimitivity blocks.…
The problem of constructing all the non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation recently has been reduced to the problem of describing all the left braces. In particular, the classification of all finite…
We describe the monodromy of dynamical Knizhnik-Zamolodchikov equations via Stokes phenomenon. It defines a family of braid groups representations by certain Stokes matrices. In particular, these Stokes matrices satisfy the Yang-Baxter…
Yang-Baxter equations define quantum integrable models. The tetrahedron and higher simplex equations are multi-dimensional generalizations. Finding the solutions of these equations is a formidable task. In this work we develop a systematic…
A computer algebra algoritm for solving the quantum Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the order \lambda^6. As an example the classification of 4x4 R-matrices is…
W. Rump showed that there exists a one-to-one correspondence between involutive right non-degenerate solutions of the Yang-Baxter equation and Rump right quasigroups. J. S. Carter, M. Elhamdadi, and M. Saito, meanwhile, introduced a…
A general functional definition of the infinite dimensional quantum R-matrix satisfying the Yang-Baxter equation is given. A procedure for extracting a finite dimensional R-matrix from the general definition is demonstrated for the…
Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any…
The aim of this paper is to show that the structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented.
We obtain a simple family of solutions to the set-theoretic Yang-Baxter equation, one which depends only on considering special endomorphisms of a finite group. We show how such an endomorphism gives rise to two non-degenerate solutions to…
A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the stochastic evolutionary equations into a backward and a…
We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS…
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.
We define a state space and a Markov process associated to the stochastic quantisation equation of Yang-Mills-Higgs (YMH) theories. The state space $\mathcal{S}$ is a nonlinear metric space of distributions, elements of which can be used as…
For any algebra two families of coloured Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated. The matrix forms…
We build the trigonometric solutions of the Yang-Baxter equation that can not be obtained from quantum groups in any direct way. The solution is obtained using the construction suggested recently from the rational conformal field theory…
The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinskis's theorem, the unitary solutions of the quantum Yang--Baxter equation can…
We study non-degenerate set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2 which are not 2-reductive. We describe an effective way of constructing such solutions using square-free 2-reductive solutions and two…