Non-weight modules over a Schr{\"o}dinger-Virasoro type algebra

TL;DR

This paper classifies all rank 1 free modules over a Schr{"o}dinger-Virasoro algebra, providing a comprehensive understanding of their structure and representations.

Contribution

It offers a complete classification of free modules of rank 1 over the Schr{"o}dinger-Virasoro type algebra, a new result in the representation theory of this algebra.

Findings

Complete classification of rank 1 free modules

Explicit descriptions of module structures

Advances understanding of Schr{"o}dinger-Virasoro algebra representations

Abstract

In this paper, we give a complete classification of all free $U(\mathbb{C}L_0 \oplus \mathbb{C}Y_0\oplus \mathbb{C}M_0)$-modules of rank 1 over a Schr{\"o}dinger-Virasoro type algebra $\mathfrak{tsv}$.