相关论文: Yangian Algebras and Classical Riemann Problems
We propose a generic framework to obtain certain types of contracted and centrally extended algebras. This is based on the existence of quadratic algebras (reflection algebras and twisted Yangians), naturally arising in the context of…
Two general families of new quantum deformed current algebras are proposed and identified both as infinite Hopf family of algebras, a structure which enable one to define ``tensor products'' of these algebras. The standard quantum affine…
Braided algebras are associative algebras endowed with a Yang-Baxter operator that satisfies certain compatibility conditions involving the multiplication. Along with Hochschild cohomology of algebras, there is also a notion of Yang-Baxter…
The search for elliptic quantum groups leads to a modified quantum Yang-Baxter relation and to a special class of quasi-triangular quasi Hopf algebras. This paper calculates deformations of standard quantum groups (with or without spectral…
Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…
We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with $\mathbb{Z}$-graded Hopf algebras. To demonstrate the approach, we provide examples for the Taft algebras and the quantum group $U_q[sl(2)]$.
We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras,…
We establish a degeneration isomorphism between quantum toroidal algebras and untwisted affine Yangians, valid for all untwisted affine Kac-Moody Lie algebras. Specifically, we prove that the affine Yangian $Y_\hbar(\mathfrak{g})$ is…
Exteded Yangian algebras of orthogonal and symplectic types are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with $so(n)$ or $sp(2m)$ symmetry. We study representations of highest weight characterized by weight…
We prove the equivalence of two presentations of deformed double current algebras associated to a complex simple Lie algebra, the first one obtained via a degeneration of affine Yangians while the other one naturally appeared in the…
Yangian-like algebras, associated with current R-matrices, different from the Yang ones, are introduced. These algebras are of two types. The so-called braided Yangians are close to the Reflection Equation algebras, arising from involutive…
Starting with a four-dimensional gauge theory approach to rational, elliptic, and trigonometric solutions of the Yang-Baxter equation, we determine the corresponding quantum group deformations to all orders in $\hbar$ by deducing their RTT…
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…
We extend to the super Yangian of the special linear Lie superalgebra $\mathfrak{sl}_{m|n}$ and its affine version certain results related to Schur-Weyl duality. We do the same for the deformed double current superalgebra of…
A self-contained description of algebraic structures, obtained by combinations of various limit procedures applied to vertex and face sl(2) elliptic quantum affine algebras, is given. New double Yangians structures of dynamical type are in…
Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general `symmetry transformation' of the `particle conserving' $R$-matrix is found such that the resulting multiparametric $R$-matrix,…
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…
Framework for constructing Fock spaces associated either with certain solutions of the quantum Yang-Baxter equation or with infinite dimensional Hecke algebra is presented. For the former case, the quantum deformed oscillator algebra…
We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter…
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…