Related papers: Yang-Baxter $\breve{R}$ matrix, Entanglement and Y…
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 construct the R-operator -- solution of the Yang-Baxter equation acting in the tensor product of two infinite-dimensional representations of Faddeev's modular double. This R-operator intertwines the product of two L-operators associated…
A three-parametric $R$-matrix satisfying a graded Yang-Baxter equation is introduced.This $R$-matrix allows us to construct new quantum supergroups which are deformations of the supergroup $GL(1/1)$ and the universal enveloping algebra…
The problem of constructing the $SL(N,\mathbb{C})$ invariant solutions to the Yang-Baxter equation is considered. The solutions ($\mathcal{R}$-operators) for arbitrarily principal series representations of $SL(N,\mathbb{C})$ are obtained in…
The Yang-Baxter equation and it's various forms have applications in many fields, including statistical mechanics, knot theory, and quantum information. Unitary solutions of the braided Yang-Baxter equation are of particular interest as…
We construct nocommutative set-theoretical solutions to the Yang--Baxter equation related to the KdV, the NLS and the derivative NLS equations. In particular, we construct several Yang--Baxter maps of KdV type and we show that one of them…
We show that braiding transformation is a natural approach to describe quantum entanglement, by using the unitary braiding operators to realize entanglement swapping and generate the GHZ states as well as the linear cluster states. A…
The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is considered. The conditions under which the algebra is associative are discussed for a general number of oscillators. Four types of solutions satisfying these…
We introduce the special set-theoretic Yang-Baxter algebra and show that it is a Hopf algebra subject to certain conditions. The associated universal R-matrix is also obtained via an admissible Drinfel'd twist. The structure of braces…
We study involutive non-degenerate set-theoretic solutions (X,r) of the Yang-Baxter equation on a finite set X. The emphasis is on the case where (X,r) is indecomposable, so the associated permutation group acts transitively on X. One of…
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…
A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit…
We consider a special class of quantum non-dynamical $R$-matrices in the fundamental representation of ${\rm GL}_N$ with spectral parameter given by trigonometric solutions of the associative Yang-Baxter equation. In the simplest case $N=2$…
We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset…
We present a one dimensional reversible block cellular automaton, where the time evolution is dictated by a period 3 cycle of update rules. At each time step a subset of the cells is updated using a four site rule with two control bits and…
We discuss applications of the $q$-characters to the computation of the $R$-matrices. In particular, we describe the $R$-matrix acting in the tensor square of the first fundamental representation of E$_8$ and in a number of other cases,…
A class of vector coherent states is derived with multiple of matrices as vectors in a Hilbert space, where the Hilbert space is taken to be the tensor product of several other Hilbert spaces. As examples vector coherent states with…
In this article, we introduce endocabling as a technique to deform involutive, non-degenerate set-theoretic solutions to the Yang-Baxter equation (``solutions'', for short) by means of $\lambda$-endomorphisms of their associated permutation…
We put forward a simple construction of genuinely entangled subspaces -- subspaces supporting only genuinely multipartite entangled states -- of any permissible dimensionality for any number of parties and local dimensions. The method uses…
At the previous congress (CRM 6), we reviewed the construction of Yang-Baxter operators from associative algebras, and presented some (colored) bialgebras and Yang-Baxter systems related to them. The current talk deals with Yang-Baxter…