On a family of non-weight modules over Virasoro-type Lie (super)algebras

TL;DR

This paper classifies certain modules over Witt-type Lie algebras and superalgebras, providing conditions for simplicity, automorphism actions, and linking to intermediate series modules via the weighting functor.

Contribution

It introduces a classification of modules over Witt-type Lie (super)algebras with specific properties, including simplicity criteria and automorphism actions.

Findings

Modules are classified under specific conditions.

Simplicity criteria are established.

Modules relate to intermediate series modules via the weighting functor.

Abstract

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 action of an automorphism on the module. Lastly, we apply the weighting functor and show that the resulting modules are intermediate series modules.