相关论文: Fifteen-vertex models with non-symmetric $R$ matri…
The free-fermion point refers to a $\operatorname{GL}(2)\times\operatorname{GL}(1)$ parametrized Yang-Baxter equation within the six-vertex model. It has been known for a long time that this is connected with the quantum group…
We investigate integrable fermionic models within the scheme of the graded Quantum Inverse Scattering Method, and prove that any symmetry imposed on the solution of the Yang-Baxter Equation reflects on the constants of motion of the model;…
We introduce non-degenerate solutions of the Yang-Baxter equation in the setting of symmetric monoidal categories. Our theory includes non-degenerate set-theoretical solutions as basic examples. However, infinite families of non-degenerate…
A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest neighbor interactions, the vertices defining the model also interact alongone of the diagonals of the lattice. Such family of…
We generalize the result of the preceeding paper and solve the Yang-Baxter equation in terms of triple systems called orthogonal and symplectic ternary systems. In this way, we found several other new solutions.
The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free…
A first aim of this paper is to give sufficient conditions on left non-degenerate bijective set-theoretic solutions of the Yang-Baxter equation so that they are non-degenerate. In particular, we extend the results on involutive solutions…
By means of an algebraic Bethe ansatz approach we study the Zamolodchikov-Fateev and Izergin-Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors…
Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation. We generalize Rump's braces to the non-commutative setting and use this new structure to study not necessarily involutive…
The graded reflection equation is investigated for the $U_{q}[osp(r|2m)^{(1)}]$ vertex model. We have found four classes of diagonal solutions with at the most one free parameter and twelve classes of non-diagonal ones with the number of…
We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form of coupled ${\rm GL}(N)$ Sklyanin elliptic algebras. Then we…
We have found a family of solvable nineteen vertex model with statistical configurations invariant by the time reversal symmetry within a systematic study of the respective Yang-Baxter relation. The Boltzmann weights sit on a degree seven…
We study involutive set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2. These solutions happen to fall into two classes -- distributive ones and non-distributive ones. The distributive ones can be effectively…
We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case of anti-flexible…
We use Cvitanovic's diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation associated with the $e_6$ and $e_7$ families of Lie algebras, and thus explain Westbury's observations about their uniform spectral…
From the q-oscillator solution to the tetrahedron equation associated with a quantized coordinate ring, we construct solutions to the Yang-Baxter equation by applying a reduction procedure formulated earlier by S. Sergeev and the first…
In this paper we present a characterization of finite simple involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation by means of left braces and we provide some significant examples.
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations…
A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where $R$-matrix solutions of the Yang--Baxter equation do not have the property of crossing unitarity. Suitably modified forms of…
The 15-vertex model of Statistical Mechanics is studied on a square domain with partially oriented boundary. With DWBC the model would reduce to the six-vertex model, but more general boundary configurations are available. After…