Related papers: Twist deformations for Yangians
We study the reduction of classical strings rotating in the deformed three-sphere truncation of the double Yang-Baxter deformation of the $\hbox{AdS}_3 \times \hbox{S}^3 \times \hbox{T}^4$ background to an integrable mechanical model. The…
Twisted Hopf algebra $sl_\xi(2)$ gives rise to a deformation of the Yangian ${\cal Y}(sl(2))$. The corresponding deformations of the integrable XXX-spin chain and the Gaudin model are discussed.
The Yang-Baxter $\sigma$-model is an integrable deformation of the principal chiral model on a Lie group $G$. The deformation breaks the $G \times G$ symmetry to $U(1)^{\textrm{rank}(G)} \times G$. It is known that there exist non-local…
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…
In this paper, we introduce the notion of an $\mathbb{N}^p$-graded birack and construct its isotope. Every involutive $\mathbb{N}^p$-graded birack gives rise to an $\mathbb{N}^p$-graded Yang-Baxter algebra. We study the relation between…
We complete the classification of $4\times 4$ regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer…
An ansatz is presented for a possible non-associative deformation of the standard Yang-Mills type gauge theories. An explicit algebraic structure for the deformed gauge symmetry is put forward and the resulting gauge theory developed. The…
We quantize the Alekseev-Meinrenken solution r to the classical dynamical Yang-Baxter equation, associated to a Lie algebra g with an element t in S^2(g)^g. Namely, we construct a dynamical twist J with nonabelian base in the sense of P.…
We consider the extensions of classical r-matrix for \kappa-deformed Poincar\'{e} algebra which satisfy modified Yang-Baxter equation. Two examples introducing additional deformation parameter (dimensionfull \frac{1}{\widetilde{\kappa}} or…
We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks, called parametric (p)-shelves and racks. Generic…
The theory of the parametric set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. The first step towards this objective is the introduction of certain generalizations of the familiar shelves and racks…
We present a method to construct "X" form unitary Yang-Baxter $\breve{R}$ matrices, which act on the tensor product space $V_{i}^{j_{1}}\otimes V_{i+1}^{j_{2}}$. We can obtain a set of entangled states for $(2j_{1}+1)\times…
Starting from a finite-dimensional representation of the Yangian $Y(\mathfrak{g})$ for a simple Lie algebra $\mathfrak{g}$ in Drinfeld's original presentation, we construct a Hopf algebra $X_\mathcal{I}(\mathfrak{g})$, called the extended…
We study quantizations of transverse slices to Schubert varieties in the affine Grassmannian. The quantization is constructed using quantum groups called shifted Yangians --- these are subalgebras of the Yangian we introduce which…
Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier…
We construct an explicit set of generators for the finite W-algebras associated to nilpotent matrices in the symplectic or orthogonal Lie algebras whose Jordan blocks are all of the same size. We use these generators to show that such…
Based on the formulation of Drinfel'd, Chari, and Pressley, a technique to analyze the structure of tensor products of the Yangian algebra representations is presented. We then apply the results to the $S$-matrix theory of the $G\otimes…
We demonstrate that the planar real-$\beta$-deformed Super-Yang--Mills theory possesses an infinitely-dimensional Yangian symmetry algebra and thus is classically integrable. This is achieved by the introduction of the twisted coproduct…
We construct type $g\ell(n)$ Yangian algebra evaluations of order $N$ embedded in Heisenberg algebras and consider their representations having a highest weight. These Yangian algebra presentations depend on $nN$ parameters. We construct…
We express the classical r-matrix of AdS/CFT in terms of tensor products involving an infinite family of generators, which takes a form suggestive of the universal expression obtained from a Yangian double. This should provide an insight…