Related papers: Irreducible Virasoro modules from irreducible Weyl…

In this paper we discuss the structure of the tensor product V'_{\alpha,\beta}\otimes L(c,h) of irreducible module from intermediate series and irreducible highest weight module over the Virasoro algebra. We generalize Zhang's…

In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a $2$-torus. The jet modules are certain natural modules over the Lie…

Let $G$ be an arbitrary additive subgroup of $C$ and $Vir[G]$ the corresponding generalized Virasoro algebra. In the present paper, irreducible weight modules with finite dimensional weight spaces over $Vir[G]$ are completely determined.…

We classify finite irreducible conformal modules over a class of infinite Lie conformal algebras ${\frak {B}}(p)$ of Block type, where $p$ is a nonzero complex number. In particular, we obtain that a finite irreducible conformal module over…

In this paper, by using the "twisting technique" we obtain a class of new modules $A_b$ over the Witt algebras $\mathcal{W}_n$ from modules $A$ over the Weyl algebras $\mathcal{K}_n$ (of Laurent polynomials) for any $b\in\mathbb{C}$. We…

The loop-Virasoro algebra is the Lie algebra of the tensor product of the Virasoro algebra and the Laurent polynomial algebra. This paper classifies irreducible Harish-Chandra modules over the loop-Virasoro algebra, which turn out to be…

Tensor product of highest weight modules and intermediate modules for Virasoro algebra have been studied around 1997. Since then the irreducibility problem for tensor product of modules is open. We consider the loop-Virasoro algebra $Vir…

In this paper, we first study two classes of Whittaker modules over the loop Witt algebra ${\mathfrak g}:=\mathcal{W}\otimes\mathcal{A}$, where $\mathcal{W}=\text{Der}({\mathbb{C}}[t])$, $\mathcal{A}={\mathbb{C}}[t,t^{-1}]$. The necessary…

In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal…

Irreducibilities of Verma modules over a class of Block type Lie algebras are completely determined. The approach developed in the present paper can be used to deal with non-weight modules.

This paper consists of two parts: (1) Using a Z[1/2]-form of Virasoro vertex operator algebra L(1/2,0) with central charge 1/2, we obtain a modular vertex operator algebra over any field F of finite characteristic different from 2. We…

We classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from…

The concept of $\lambda$-differential operators is a natural generalization of differential operators and difference operators. In this paper, we determine the $\lambda$-differential Lie algebraic structure on the Witt algebra and the…

In this paper, we consider the classification of irreducible ${\bf Z}$- and ${\bf Z}^2$-graded modules with finite dimensional homogeneous subspaces over the Virasoro-like algebra. We first prove that such a module is a uniformly bounded…

We introduce a category B of bounded modules for the toroidal Lie algebras and study irreducible modules in B. We show that one of the irreducible modules in this category, L(T_0), admits a structure of a vertex operator algebra. We prove…

In this article, certain indecomposable Virasoro modules are studied. Specifically, the Virasoro mode L_0 is assumed to be non-diagonalisable, possessing Jordan blocks of rank two. Moreover, the module is further assumed to have a highest…

In this paper we classify extensions between irreducible finite conformal modules over the Virasoro algebra, over the current algebras and over their semidirect sums.

In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $\mathbb{Z}^+$-graded Lie conformal algebras…

It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains…

In this paper we study the representations of loop Affine-Virasoro Algebras. As they have canonical triangular decomposition, we define Verma modules and its irreducible quotients. We give necessary and sufficient condition for an…