# Extensions of finite irreducible modules of Lie conformal algebras $\mathcal{W}(a,b)$ and some Schr\"{o}dinger-Virasoro type Lie conformal algebras

## TL;DR

This paper classifies all possible extensions of finite irreducible modules over certain Lie conformal algebras, including $ ext{W}(a,b)$ and Schr"odinger-Virasoro type algebras, advancing understanding of their module structures.

## Contribution

It provides a complete classification of extensions of finite irreducible modules for $ ext{W}(a,b)$ and Schr"odinger-Virasoro type Lie conformal algebras, a novel comprehensive result.

## Key findings

- Classified all extensions of modules over $ ext{W}(a,b)$.
- Characterized all extensions over Schr"odinger-Virasoro type algebras.
- Enhanced understanding of module structures in Lie conformal algebras.

## Abstract

Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we give a complete classification of extensions of finite irreducible conformal modules of $\mathcal{W}(a,b)$. With a similar method, we characterize all extensions of finite irreducible conformal modules of Schr\"{o}dinger-Virasoro type Lie conformal algebras $TSV(a,b)$ and $TSV(c)$.