Related papers: Generalized $ \widetilde{W} $ algebras
Let $e$ be an arbitrary even nilpotent element in the general linear Lie superalgebra $\mathfrak{gl}_{M|N}$ and let $\mathcal{W}_e$ be the associated finite $W$-superalgebra. Let $Y_{m|n}$ be the super Yangian associated to the Lie…
A Yang-Baxter relation-based formalism for generalized quantum affine algebras with the structure of an infinite Hopf family of (super-) algebras is proposed. The structure of the infinite Hopf family is given explicitly on the level of $L$…
We obtain a complete classification of minimal simple unitary $W$-algebras.
Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…
This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.
A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…
We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…
In this paper we present a systematic study of $W$ algebras from the Hamiltonian reduction point of view. The Drinfeld-Sokolov (DS) reduction scheme is generalized to arbitrary $sl_2$ embeddings thus showing that a large class of W algebras…
The central extension of a new infinite dimensional algebra which has both $W_\infty$ and affine $sl(2,R)$ as subalgebras is found. The critical dimension of the corresponding string model is $D=5$.
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…
In this paper, we study the derivations, central extensions and the automorphisms of the infinite-dimensional Lie algebra W which appeared in [8] and Dong-Zhang's recent work [22] on the classification of some simple vertex operator…
In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…
We give some evidences which imply that W(1+infinity) algebra describes the symmetry behind AGT(-W) conjecture: a correspondence between the partition function of N=2 supersymmetric quiver gauge theories and the correlators of Liouville…
Wawamoto generalized the Witt algebra using Laurent extension of polynomial ring. We construct the generalized Witt algebra $W(g_p,n)$ by using an additive map $g_p$ from a set of integers into a field of characteristic zero where $1\leq p…
We provide a new foundational approach to the generalization of terms up to equational theories. We interpret generalization problems in a universal-algebraic setting making a key use of projective and exact algebras in the variety…
Let $\mathfrak{g}=\mathfrak{gl}_{M|N}(\mathbb{k})$ be the general linear Lie superalgebra over an algebraically closed field $\mathbb{k}$ of characteristic zero. Fix an arbitrary even nilpotent element $e$ in $\mathfrak{g}$ and let…
We show that a wide class of $W$-(super)algebras, including $W_N^{(N-1)}$, $U(N)$-superconformal as well as $W_N$ nonlinear algebras, can be linearized by embedding them as subalgebras into some {\em linear} (super)conformal algebras with…
We investigate in detail relationships between the set ${\mathfrak B}^\infty$ of all infinite ``biconvex'' sets in the positive root system $\Delta_+$ of an arbitrary untwisted affine Lie algebra ${\mathfrak g}$ and the set ${\mathcal…
Let $H^{\infty}(E)$ be a non commutative Hardy algebra, associated with a $W^*$-correspondence $E$. In this paper we construct factorizations of inner-outer type of the elements of $H^{\infty}(E)$ represented via the induced representation,…
The set of modular invariants that can be obtained from Galois transformations is investigated systematically for WZW models. It is shown that a large subset of Galois modular invariants coincides with simple current invariants. For…