Related papers: Derivation of R-matrix from local Hamiltonian dens…
We provide explicit presentations of members of a suite of R matrices arising from the (\dot{0}_m|\alpha) representations of the quantum superalgebras U_q[gl(m|1)]. Our algorithm constructs both trigonometric and quantum R matrices; all of…
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter…
For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra…
We survey the matrix product solutions of the Yang-Baxter equation obtained recently from the tetrahedron equation. They form a family of quantum $R$ matrices of generalized quantum groups interpolating the symmetric tensor representations…
In this paper, we determine all unitary solutions to the Yang-Baxter equation in dimension four. Quantum computation motivates this study. This set of solutions will assist in clarifying the relationship between quantum entanglement and…
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.
A coloured braid group representation (CBGR) is constructed with the help of some modified universal ${\cal R}$-matrix, associated to $U_q(gl(2))$ quantised algebra. Explicit realisation of Faddeev-Reshetikhin-Takhtajan (FRT) algebra is…
We show that Belavin's solutions of the quantum Yang--Baxter equation can be obtained by restricting an infinite $R$-matrix to suitable finite dimensional subspaces. This infinite $R$-matrix is a modified version of the Shibukawa--Ueno…
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…
A general functional definition of the infinite dimensional quantum $R$-matrix satisfying the Yang-Baxter equation is given. A procedure for the extracting a finite dimensional $R$-matrix from the general definition is demonstrated in a…
Generalization of the quantum Yang-Baxter equation solutions to an arbitrary grading is studied. The noncommutative differential calculi corresponding to such solutions is considered. The connection with the ordinary and supersymmetric…
In this paper, the different operator forms of classical Yang-Baxter equation are given in the tensor expression through a unified algebraic method. It is closely related to left-symmetric algebras which play an important role in many…
We present a simple but explicit example of a recent development which connects quantum integrable models with Schubert calculus: there is a purely geometric construction of solutions to the Yang-Baxter equation and their associated…
In this article, we develop a geometric method to construct solutions of the classical Yang-Baxter equation, attaching to the Weierstrass family of plane cubic curves and a pair of coprime positive integers, a family of classical…
We have constructed series of the spectral parameter dependent solutions to the Yang-Baxter equations defined on the tensor product of reducible representations with symmetry of quantum algebra. These series are produced as descendant…
We present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension. This approach, inspired in the Lie (super)algebra structure, is explicitly applied to the particular case of…
In order to examine the simulation of integrable quantum systems using quantum computers, it is crucial to first classify Yang-Baxter operators. Hietarinta was among the first to classify constant Yang-Baxter solutions for a two-dimensional…
In the classification of solutions of the Yang--Baxter equation, there are solutions that are not deformations of the trivial solution (essentially the identity). We consider the algebras defined by these solutions, and the corresponding…
We construct spectral parameter dependent R-matrices for the quantized enveloping algebras of twisted affine Lie algebras. These give new solutions to the spectral parameter dependent quantum Yang-Baxter equation.
We construct invertible spectral parameter dependent Yang-Baxter solutions ($R$-matrices) by Baxterizing constant non-invertible Yang-Baxter solutions. The solutions are algebraic (representation independent). They are constructed using…