Weight modules for map (super)algebra related to the Virasoro algebra

TL;DR

This paper classifies jet modules for certain Lie superalgebras related to the Virasoro algebra and introduces a method to classify all simple cuspidal modules for these algebras and their map superalgebra extensions.

Contribution

It provides a classification of jet modules for a class of Lie superalgebras and a new method for classifying simple cuspidal modules for these algebras and their map superalgebras.

Findings

Classification of jet modules for $rak{L}$ and related superalgebras.

A conceptual method for classifying simple cuspidal modules.

Extension of classification results to map superalgebras.

Abstract

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 a concept method to classify all simple cuspidal modules for $\mathfrak{L}$ and the map superalgebras, which are of the form $\mathfrak{L}\otimes R$, where $R$ is a Noetherian unital supercommutative associative superalgebra.