Related papers: On exactly solvable Yang-Baxter models and enhance…
Many of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertex- and IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these, representations of a two-colour…
Quantum universal enveloping algebras, quantum elliptic algebras and double (deformed) Yangians provide fundamental algebraic structures relevant for many integrable systems. They are described in the FRT formalism by R-matrices which are…
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…
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
We study a flat connection defined on the open-closed deformation space of open string mirror symmetry for type II compactifications on Calabi-Yau threefolds with D-branes. We use flatness and integrability conditions to define…
We complete the classification of $4\times 4$ regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer…
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;…
The dimer model on a strip is considered as a Yang-Baxter \mbox{integrable} six vertex model at the free-fermion point with crossing parameter $\lambda=\tfrac{\pi}{2}$ and quantum group invariant boundary conditions. A one-to-many mapping…
Modified $r$-matrices are solutions of the modified classical Yang-Baxter equation, introduced by Semenov-Tian-Shansky, and play important roles in mathematical physics. In this paper, first we introduce a cohomology theory for modified…
The Yang-Baxter $\sigma$-model is an integrable deformation of the principal chiral model on a Lie group $G$. The deformation breaks the $G \times G$ symmetry to $U(1)^{\textrm{rank}(G)} \times G$. It is known that there exist non-local…
We classify all regular solutions of the Yang-Baxter equation of eight-vertex type. Regular solutions correspond to spin chains with nearest-neighbour interactions. We find a total of four independent solutions. Two are related to the usual…
An ansatz is presented for a possible non-associative deformation of the standard Yang-Mills type gauge theories. An explicit algebraic structure for the deformed gauge symmetry is put forward and the resulting gauge theory developed. The…
We investigate different Hopf algebras associated to Yang's solution of quantum Yang-Baxter equation. It is shown that for the precise definition of the algebra one needs the commutation relations for the deformed algebra of formal currents…
The most common geometric interpretation of the Yang-Baxter equation is by braids, knots and relevant Reidemeister moves. So far, cubes were used for connections with the third Reidemeister move only. We will show that there are…
Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…
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…
Starting with a four-dimensional gauge theory approach to rational, elliptic, and trigonometric solutions of the Yang-Baxter equation, we determine the corresponding quantum group deformations to all orders in $\hbar$ by deducing their RTT…
The pioneering work of Rump, which proved Gateva-Ivanova's conjecture concerning the decomposability of square-free solutions to the Yang-Baxter equation, significantly motivated further research into the associated squaring map $T$. This…
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…