Related papers: Modules over the algebra $\mathcal{V}ir(a,b)$

Let $\mathbb{C}_q$ be a non-commutative Laurent polynomial ring associated with a $(n+1)\times (n+1)$ rational quantum matrix $q$. Let $\mathfrak{sl}_d(\mathbb{C}_q)\oplus HC_1(\mathbb{C}_q)$ be the universal central extension of Lie…

In this paper, we classify all simple weight modules with finite-dimensional weight spaces over the $N=2$ Ramond algebra. Any such module $V$ is either a simple highest weight module or a simple lowest weight module, or a simple cuspidal…

We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra not of the type A(2k,2l)^{(4)}. We obtain the character formula for a simple module with a generic…

Lie algebras formed via semi-direct sums of the Witt algebra $\text{Der}(\mathbb{C}[t,t^{-1}])$ and its modules have become increasingly prominent in both physics and mathematics in recent years. In this paper, we complete the study of…

We construct an example of a regular algebra over $\mathbb C$ of dimension $d$ and a rank $r$ projective module over it which is not generated by $d+r-1$ elements. This strengthens an example by Swan over the field of real numbers.

We consider the category of Whittaker modules for the Lie superalgebra $W_{m,n}$ of vector fields on $\mathbb{C}^{(m|n)}$. For any $\mathbf{a}\in \mathbb{C}^m$ we show the equivalence between the blocks $\Omega_{\mathbf…

It is proved that uniformly bounded simple modules over higher rank super-Virasoro algebras are modules of the intermediate series, and that simple modules with finite dimensional weight spaces are either modules of the intermediate series…

In this paper, we classify all finite irreducible conformal modules over a class of Lie conformal algebras $\mathcal{W}(b)$ with $b\in\mathbb{C}$ related to the Virasoro conformal algebra. Explicitly, any finite irreducible conformal module…

Let $d>1$ be an integer. In 1986, Shen defined a class of weight modules $F^\alpha_b(V)$ over the Witt algebra $\mathcal{W}_d$ for $\a\in\C^d$, $b\in\C$, and an irreducible module $ V$ over the special linear Lie algebra $\sl_d$. In 1996,…

We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some…

For a simple Lie algebra $\mathfrak{g}$ of type $A_n,B_n,C_n$ or $D_n$, we give a characterization of the set of dominant integral weights $\lambda$ such that for any rational point $\mu$ in the fundamental Weyl chamber, $2\lambda-\mu$ is a…

The main result of this paper is the characterization of zero-level integrable finite weight modules, over twisted affine Lie superalgebras. We prove that such a module is parabolically induced from a module which is obtained, in a…

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over $\mathbb{C}$. A $\operatorname{Y}(\mathfrak{g})$-module is said to be weight if it is a weight $\mathfrak{g}$-module. We give a complete classification of simple weight…

Let $n>1$ be an integer, $\alpha\in{\mathbb C}^n$, $b\in{\mathbb C}$, and $V$ a $\mathfrak{gl}_n$-module. We define a class of weight modules $F^\alpha_{b}(V)$ over $\sl_{n+1}$ using the restriction of modules of tensor fields over the Lie…

We classify all non-abelian groups G such that there exists a pair (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional under two assumptions: the square…

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…

Let ${\mathcal W}_n$ be the Lie algebra of polynomial vector fields. We classify simple weight ${\mathcal W}_n$-modules $M$ with finite weight multiplicities. We prove that every such nontrivial module $M$ is either a tensor module or the…

Let $n\geq 2$ be an integer, $S_n$ be the Lie algebra of vector fields on $\mathbb{C}^n$ with zero divergence, and $D_n$ be the Weyl algebra over the polynomial algebra $A_n=\mathbb{C}[t_1,t_2,\cdots,t_n]$. In this paper, we study the…

A weight module of a basic Lie superalgebra is called finite if all of its weight spaces are finite dimensional, and it is called bounded if there is a uniform bound on the dimension of a weight space. The minimum bound is called the degree…

We define global and local Weyl modules for $q \otimes A$, where $q$ is the queer Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}-$algebra. We prove that global Weyl modules are universal highest weight objects in…