Related papers: Tensor modules over Witt superalgebras

Let $A_{m,n}$ be the tensor product of the polynomial algebra in $m$ even variables and the exterior algebra in $n$ odd variables over the complex field $\C$, and the Witt superalgebra $W_{m,n}$ be the Lie superalgebra of superderivations…

For an irreducible module $P$ over the Weyl algebra $\mathcal{K}_n^+$ (resp. $\mathcal{K}_n$) and an irreducible module $M$ over the general liner Lie algebra $\mathfrak{gl}_n$, using Shen's monomorphism, we make $P\otimes M$ into a module…

Let $A_{m,n}$ be the tensor product of the Laurient polynomial algebra in $m$ even variables and the exterior algebra in $n$ odd variables over the complex field $\bC$, and the Witt superalgebra $W_{m,n}$ be the Lie superalgebra of…

Let $W_n^+$ be the Lie algebra of the Lie algebra of vector fields on $\C^n$. In this paper, we classify all simple bounded weight $W_n^+$ modules. Any such module is isomorphic to the simple quotient of a tensor module $F(P,M)=P\otimes M$…

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 $d\ge1$ be an integer, $W_d$ and $\mathcal{K}_d$ be the Witt algebra and the weyl algebra over the Laurent polynomial algebra $A_d=\mathbb{C} [x_1^{\pm1}, x_2^{\pm1}, ..., x_d^{\pm1}]$, respectively. For any $\mathfrak{gl}_d$-module $M$…

In this paper, we classify simple strong Harish-Chandra modules over the Lie superalgebra $W_{m,n}$ of vector fields on $\C^{m|n}$. Any such module is the unique simple submodule of some tensor module $F(P,V)$ for a simple weight module $P$…

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…

Simple modules for the restricted Witt superalgebra $W(m,n,1)$ are considered. Conditions are provided for the restricted and nonrestricted Kac modules to be simple.

We classify Jet modules for the Lie (super)algebras $\mathfrak{L}=W\ltimes(\mathfrak{g}\otimes\mathbb{C}[t,t^{-1}])$, where $W$ is the Witt algebra and $\mathfrak{g}$ is a Lie superalgebra with an even diagonlizable derivation. Then we give…

In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras $W_n$, we explicitly describe supports of such modules. We also obtain some descriptions on the…

In this paper, we begin the study of highest weight representations of the quantized enveloping superalgebra ${\mathfrak U}_q {\mathfrak p}_n$ of type $P$. We introduce a Drinfeld-Jimbo representation and establish a…

We classify all simple strong Harish-Chandra modules for the Lie superalgebra $W(m,n)$. We show that every such module is either strongly cuspidal or a module of the highest weight type. We construct tensor modules for $W(m,n)$, which are…

In this thesis we classify modules over a Witt-type Lie algebra and superalgebra such that when considered as modules of $\mathcal{U}(\mathfrak{h})$ they are free of rank 1. We provide sufficient conditions for simplicity, and compute the…

Let $n\ge2$ be an integer, $\mathcal{K}_n$ the Weyl algebra over the Laurent polynomial algebra $A_n=\mathbb{C} [x_1^{\pm1}, x_2^{\pm1}, ..., x_n^{\pm1}]$, and $\mathbb{S}_n$ the Lie algebra of divergence zero vector fields on an…

We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…

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…

We introduce a new class of simple Lie algebras $W(n,m)$ that generalize the Witt algebra by using "exponential" functions, and also a subalgebra $W^*(n,m)$ thereof; and we show each derivation of $W^*(1,0)$ can be written as a sum of an…

In this paper, we study weight representations over the Schr{\"o}dinger Lie algebra $\mathfrak{s}_n$ for any positive integer $n$. It turns out that the algebra $\mathfrak{s}_n$ can be realized by polynomial differential operators. Using…

In this paper, we construct a family of non-weight modules over the untwisted $N=2$ superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra (modulo the center) are free of rank $2$. We give a…