Related papers: Lax Operator for the Quantised Orthosymplectic Sup…
We study the Yang-Baxter operator for the vector representation $V_m$ of the quantum group $U_q(sl_m)$. We consider the one-term Yang-Baxter homology with coefficients in $V_m$-modules and provide a direct sum decomposition of the one term…
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…
The exotic quantum double and its universal R-matrix for quantum Yang-Baxter equation are constructed in terms of Drinfeld's quantum double theory.As a new quasi-triangular Hopf algebra, it is much different from those standard quantum…
We present an approach to evaluate the full operatorial Q-system of all $\mathfrak{u}(p,q|r+s)$-invariant spin chains with representations of Jordan-Schwinger type. In particular, this includes the super spin chain of planar $\mathcal{N}=4$…
Motivated by the study of the operator forms of the constant classical Yang-Baxter equation given by Semonov-Tian-Shansky, Kupershmidt and the others, we try to construct the rational solutions of the classical Yang-Baxter equation with…
The (G, \theta)-Lie algebras are structures which unify the Lie algebras and Lie superalgebras. We use them to produce solutions for the quantum Yang-Baxter equation. The constant and the spectral-parameter Yang-Baxter equations and…
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…
The central object of the quantum algebraic approach to the study of quantum integrable models is the universal $R$-matrix, which is an element of a completed tensor product of two copies of quantum algebra. Various integrability objects…
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…
In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator…
We reformulate the method recently proposed for constructing quasitriangular Hopf algebras of the quantum-double type from the R-matrices obeying the Yang-Baxter equations. Underlying algebraic structures of the method are elucidated and an…
A counterpart of the modular double for quantum superalgebra $\cU_q(\osp(1|2))$ is constructed by means of supersymmetric quantum mechanics. We also construct the $R$-matrix operator acting in the corresponding representations, which is…
Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of some real three dimensional Lie algebras. The Jacobi operators of these quantum algebras are studied in semiclassical approximation.
We construct $2^n$-families of solutions of the Yang-Baxter equation from $n$-products of three-dimensional $R$ and $L$ operators satisfying the tetrahedron equation. They are identified with the quantum $R$ matrices for the Hopf algebras…
Conformal classical Yang-Baxter equation and $S$-equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras. In this paper, they are interpreted in terms of a kind of operators, namely,…
For a reductive Lie algebra g, its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients in the quantum finite W-algebra W(g,f). We show that for the classical linear Lie…
In this paper, first we recall the notion of Hom-Jordan superalgebras and study their representations. We define the Yang-Baxter equation in a Hom-Jordan superalgebra. Additionally, we extend the connections between $\mathcal {O}$-operators…
We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed)…
We derive the integral operator form for the general rational solution of the Yang-Baxter equation with $s\ell(2|1)$ symmetry. Considering the defining relations for the kernel of the R-operator as a system of second order differential…
Exteded Yangian algebras of orthogonal and symplectic types are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with $so(n)$ or $sp(2m)$ symmetry. We study representations of highest weight characterized by weight…