Related papers: Parametric set-theoretic Yang-Baxter equation: p-r…
We study a generalisation of the set-theoretic Yang-Baxter equation and investigate the connection between its solutions and matrix refactorisation problems. We refer to such solutions as scalene Yang-Baxter maps. Moreover, we construct…
Recently, researchers have proposed the Asymmetric Bethe ansatz method - a theoretical tool that extends the scope of Bethe ansatz-solvable models by "breaking" partial mirror symmetry via the introduction of a fully reflecting boundary.…
The notion of matching Rota-Baxter algebras was recently introduced by Gao, Guo and Zhang [{\em J. Algebra} 552 (2020) 134-170] motivated by the study of algebraic renormalization of regularity structures. The concept of matching…
The definitions of the main notions related to the quantum inverse scattering methods are given. The Yang-Baxter equation and reflection equations are derived as consistency conditions for the factorizable scattering on the whole line and…
We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the…
We propose a new generalization of the Yang-Baxter equation, where the R-matrix depends on cluster $y$-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the…
We connect generalizations of Poisson algebras with the classical and associative Yang-Baxter equations. In particular, we prove that solutions of the classical Yang-Baxter equation on a vector space V are equivalent to ``twisted'' Poisson…
We present rational Lax representations for one-component parametric quadrirational Yang-Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrices of a general class of non-abelian involutive Yang-Baxter…
We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent $R_{ij}(u)$-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation…
Let $(X, r)$ be any set-theoretical non-degenerate solution of the Yang-Baxter equation and $(X, \tilde r)$ be the derived solution of $(X, r)$. As for any braided vector space $(W_{X, r}, c)$ associated to $(X, r)$, is it possible to find…
For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum…
The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R(p), where $p$ stands for a set of mutually commuting variables. A family of SL(n)-type solutions of this equation provides a new realization of the…
We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the…
For the last fifteen years quantum superalgebras have been used to model supersymmetric quantum systems. A class of quasi-triangular Hopf superalgebras, they each contain a universal $R$-matrix, which automatically satisfies the…
We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form of coupled ${\rm GL}(N)$ Sklyanin elliptic algebras. Then we…
The general rational solution of the Yang-Baxter equation with the symmetry algebra sl(2) can be represented as the product of the simpler building blocks denoted as R-operators. The R-operators are constructed explicitly and have simple…
Given a right-non-degenerate set-theoretic solution $(X,r)$ to the Yang-Baxter equation, we construct a whole family of YBE solutions $r^{(k)}$ on $X$ indexed by its reflections $k$ (i.e., solutions to the reflection equation for $r$). This…
We find a method to construct iteratively from a non-degenerate involutive set-theoretic solution of the Yang-Baxter equation an infinite family of very large non-degenerate involutive set-theoretic solutions. In case the initial solution…
Recent study suggests that there are natural connections between quantum information theory and the Yang--Baxter equation. In this paper, in terms of the generalized almost-complex structure and with the help of its algebra, we define the…
The interplay between set-theoretic solutions of the Yang--Baxter equation of Mathematical Physics, skew braces, regular subgroups, and Hopf--Galois structures has spawned a considerable body of literature in recent years. In a recent…