Related papers: W-algebras, Gaussian Free Fields and $\mathfrak{g}…
Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as $W$-algebras. Known examples include contractions of pairs of the Virasoro algebra, its $N=1$…
$L_{\infty}$ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry…
We study the structure and representation theory of the principal W-algebra $\mathsf{W}^{\mathsf{k}}_{\mathrm{pr}}$ of $\mathsf{V}^{\mathsf{k}}(\mathfrak{psl}_{2|2})$. The defining operator product expansions are computed, as is the Zhu…
We investigate the algebraic structure of integrable hierarchies that, we propose, underlie models of $W$-gravity coupled to matter. More precisely, we concentrate on the dispersionless limit of the topological subclass of such theories, by…
To each skew-gentle algebra, one can assign a gentle algebra in terms of combinatorial data. In order to relate the structures of the two algebras, we establish a homological epimorphism and a recollement of derived module categories. This…
Recently, a new generalized family of infinite-dimensional $ \widetilde{W} $ algebras, each associated with a particular element of a commutative subalgebra of the $ W_{1+\infty} $ algebra, was described. This paper provides a comprehensive…
This article is founded on two fundamental principles: the principle field equations introduced in Refs. \cite{S, S1, S2} and the Fock-Ivanenko covariant derivatives \cite{FI, F}. The former yields the equations of motion for free fields of…
Two approaches (TW and ASvM) to derivation of integrable differential equations for random matrix probabilities are compared. Both methods are rewritten in such a form that simple and explicit relations between all TW dependent variables…
A gauged $SU_q(2)$ theory is characterized by two dual algebras, the first lying close to the Lie algebra of SU(2) while the second introduces new degrees of freedom that may be associated with non-locality or solitonic structure. The first…
We classify the finite dimensional irreducible representations of rectangular finite $W$-algebras, i.e., the finite $W$-algebras $U(\mathfrak{g}, e)$ where $\mathfrak{g}$ is a symplectic or orthogonal Lie algebra and $e \in \mathfrak{g}$ is…
Representations of the Schlessinger-Stasheff's associative homotopy Lie algebras in the spaces of higher-order differential operators are analyzed; in particular, a remarkable identity for the Wronskian determinants is obtained. The…
The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra $\goth g$ there exists a complete set of commuting polynomials on its dual space $\goth g^*$. In terms of the theory of integrable…
The quantum toroidal algebra of $gl_1$ provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed W-algebras including non-principal cases…
The dynamical algebra associated to a family of Isospectral Oscillator Hamiltonians, named {\it Distorted Heisenberg Algebra} because its dependence on a distortion parameter $W \geq 0$, has been recently studied. The connection of this…
We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant…
It is argued that chiral algebras of conformal field theory possess a W-algebra structure. A survey of explicitly known W-algebras and their constructions is given. (Talk given at the XIX International Colloquium on ``Group Theoretical…
Let $\mathfrak g$ be a simple Lie algebra over $\mathbb C$ and let $e \in \mathfrak g$ be nilpotent. We consider the finite $W$-algebra $U(\mathfrak g,e)$ associated to $e$ and the problem of determining the variety $\mathcal E(\mathfrak…
Let $\alpha$ be a polynomial Poisson bivector on a finite-dimensional vector space $V$ over $\mathbb{C}$. Then Kontsevich [K97] gives a formula for a quantization $f\star g$ of the algebra $S(V)^*$. We give a construction of an algebra with…
Let $X$ be a complex manifold, $\pi: E \rightarrow X$ a locally trivial holomorphic fibration with fiber $F$, and $\mathfrak{g}$ a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization…
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…