Related papers: Twisted Yang-Baxter equations for linear quantum (…
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…
It is demonstrated how chains of twists for classical Lie algebras induce the new twist deformations (the deformed Yangians) that quantize the generalized rational solutions of the classical Yang-Baxter equation. For the case of Y(g) with…
We construct an algebra morphism from the elliptic quantum group $E_{\tau,\eta}(sl_2)$ to a certain elliptic version of the ``quantum groups in higher genus'' studied by V. Rubtsov and the first author. This provides an embedding of…
The Baxterization process for the dynamical Yang-Baxter equation is studied. We introduce the local dynamical Hecke ,Temperley-Lieb and Birman-Murakami-Wenzl operators, then by inserting spectral parameters, from each representation of…
In this paper we study the problem of classification of indecomposable solutions of the Yang-Baxter equation. Using a scheme proposed by Bachiller, Ced\'o, and Jespers, and recent advances in the classification of braces we classify all…
In the first part, we focus on indecomposable involutive solutions of the Yang-Baxter equation whose permutation group forces them to be uniconnected. Indecomposable involutive solutions with a permutation group isomorphic to a dihedral…
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 have found some new solutions of both rational and trigonometric types by rewriting Yang-Baxter equation as a triple product equation in a vector space of matrices.
Formulating quantum integrability for nonultralocal models (NM) parallel to the familiar approach of inverse scattering method is a long standing problem. After reviewing our result regarding algebraic structures of ultralocal models, we…
Enhanced Yang-Baxter operators give rise to invariants of oriented links. We expand the enhancing method to generalized Yang-Baxter operators. At present two examples of generalized Yang-Baxter operators are known and recently three types…
The intertwiner of the quantized coordinate ring $A_q(sl_3)$ is known to yield a solution to the tetrahedron equation. By evaluating their $n$-fold composition with special boundary vectors we generate series of solutions to the Yang-Baxter…
In this paper we discuss and characterize several set-theoretic solutions of the Yang-Baxter equation obtained using skew lattices, an algebraic structure that has not yet been related to the Yang-Baxter equation. Such solutions are…
We find new solutions to the Yang-Baxter equations with the $R$-matrices possessing $sl_q(2)$ symmetry at roots of unity, using indecomposable representations. The corresponding quantum one-dimensional chain models, which can be treated as…
An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra underlying…
We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the…
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…
A parametrized Yang-Baxter equation is usually defined to be a map from a group to a set of R-matrices, satisfying the Yang-Baxter commutation relation. These are a mainstay of solvable lattice models. We will show how the parameter space…
A review of some recent results on the dynamical theory of the Yang-Baxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics. The…
We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the…
We construct integrable modifications of 2d lattice gauge theories with finite gauge groups.