Related papers: The hyperbolic modular double and the Yang-Baxter …
The aim of this review is to present the list of by now a significant collection of quantum integrable models, ultralocal as well as nonultralocal, in a systematic way stressing on their underlying unifying algebraic structures. We restrict…
We study integrable deformations of two-dimensional non-linear sigma-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2,R) bi-Yang-Baxter…
We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the Yang-Baxter equation and to express the corresponding…
In this note, we propose a decomposition of the quantum matrix group SL$_q^+(2,\mathbb{R})$ as (deformed) exponentiation of the quantum algebra generators of Faddeev's modular double of $\text{U}_q(\mathfrak{sl}(2, \mathbb{R}))$. The…
We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized generalized…
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…
We study Zamolodchikov algebras whose commutation relations are described by Belavin matrices defining a solution of the Yang-Baxter equation (Belavin $R$-matrices). Homomorphisms of Zamolodchikov algebras into dynamical algebras with…
Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on…
Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space.…
In this paper we construct a new quantum double by endowing the l-state bosonalgebra with a non-trivial Hopf algebra structure,which is not a q-deformation of the Lie algebra or superalgebra.The universal R-matrix for the Yang-Baxter…
We study integrable models in the context of the recently discovered Gauge/YBE correspondence, where the Yang-Baxter equation is promoted to a duality between two supersymmetric gauge theories. We study flavored elliptic genus of 2d…
This brief review surveys recent progress driven by the gauge/Yang-Baxter equation (YBE) correspondence. This connection has proven to be a powerful tool for discovering novel integrable lattice spin models in statistical mechanics by…
Recently, Ferri and Sciandra introduced two equivalent algebraic structures, matched pair of actions on an arbitrary Hopf algebra and Yetter-Drinfeld brace. In fact, they equivalently produce braiding operators on Hopf algebras satisfying…
We find a family of solutions to Zamolodchikov's tetrahedral algebra corresponding to the fermionic R-operator for the free fermion model of the difference type in one of the spectral parameters, construct an extension of the R-operator for…
Motivated by recent work on Hom-Lie algebras, a twisted version of the Yang-Baxter equation, called the Hom-Yang-Baxter equation (HYBE), was introduced by the author in an earlier paper. In this paper, several more classes of solutions of…
In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of…
Based on the tetrahedral Zamolodchikov algebra, we prove the Yang-Baxter equation for the R-matrix of 1-D SU(n) Hubbard model. Furthermore, we present a generalization of the model.
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…
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…
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…