Simple weight modules with finite-dimensional weight spaces over Witt superalgebras

Abstract

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 superderivations of $A_{m,n}$. In this paper, we classify the simple weight $W_{m,n}$ modules with finite-dimensional weight spaces with respect to the standard Cartan algebra of $W_{m,0}$. Every such module is either a simple quotient of a tensor module or a module of highest weight type.

References in corpus (2)

• Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus
• Classification of simple bounded weight modules of the Lie algebra of vector fields on $\C^n$

Cited by in corpus (6)

• Classification of simple bounded weight modules of the Lie algebra of vector fields on $\C^n$
• bounded weight modules over the Lie superalgebra of Cartan W-type
• Weight modules for map (super)algebra related to the Virasoro algebra
• Classification of simple strong Harish-Chandra modules over the Lie superalgebra of vector fields on $\C^{m|n}$
• Irreducible Modules for Super-Virasoro Algebras from Algebraic D-Modules
• Irreducible Jet modules for the vector field Lie algebra on ${\mathbb{S}}^1\times \mathbb{C}$