Related papers: Twisted Affine Yangian and Rectangular $W$-algebra…
We present a connection between W-algebras and Yangians, in the case of gl(N) algebras, as well as for twisted Yangians and/or super-Yangians. This connection allows to construct an R-matrix for the W-algebras, and to classify their…
With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian…
In the previous paper, we constructed two kinds of edge contractions for the affine super Yangian and a homomorphism from the affine super Yangian to the universal enveloping algebra of a $W$-superalgebra of type $A$. In this article, we…
Let G be a group and let W be an algebra over a field K. We will say that W is a G-graded twisted algebra if W can be written as a direct sum over the elements of G of one dimensional K-vector spaces. It is also assumed that W has no…
The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with gl(N). We prove a classification theorem for finite-dimensional irreducible representations of the twisted q-Yangians associated with the…
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…
The affine Yangian of $\mathfrak{gl}_1$ is known to be isomorphic to ${\cal W}_{1+\infty}$, the $W$-algebra that characterizes the bosonic higher spin -- CFT duality. In this paper we propose defining relations of the Yangian that are…
We show that the class of twisted fractionally Calabi-Yau algebras of finite global dimension coincides with the stable endomorphism algebras of $d$-cluster tilting modules over $d$-representation-finite algebras. This is an application of…
We present a self-contained formulation of the Nonlinear Schrodinger hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F. algebra). The link between Yangian Y(gl(N)) and finite W(gl(pN),N.gl(p)) algebras is also…
In 2016, Etingof defined the notion of a Yangian in a symmetric tensor category and posed the problem to study them in the context of Deligne categories. This problem was studied by Kalinov in 2020 for the Yangian $Y(\mathfrak{gl}_t)$ of…
Given a polynomial $W$ with an isolated singularity, we can consider the Jacobian ring as an invariant of the singularity. If in addition we have a group action on the polynomial ring with $W$ fixed, we are led to consider the twisted…
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…
In this paper we introduce the shifted twisted Yangian of type {\sf AI}, following the work of Lu--Wang--Zhang, and we study their semiclassical limits, a class of Poisson algebras. We demonstrate that they coincide with the Dirac…
We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine $\imath$quantum groups (associated with split Satake diagrams). These new…
We introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the quantum Yang-Baxter equation is constructed arising from any…
We show that, in the open Hubbard model with integrable boundary conditions, the bulk Yangian symmetry is broken to a twisted Yangian. We prove that the associated charges commute with the Hamiltonian and the reflection matrix, and that…
The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…
We give explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra and of its twisted analogues, corresponding to symplectic and orthogonal Lie algebras. In particular, we develop the fusion…
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 consider the (finite) $W$-algebra $W_{m|n}$ attached to the principal nilpotent orbit in the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb C)$. Our main result gives an explicit description of $W_{m|n}$ as a certain…