Extensions of Schr\"odinger-Virasoro conformal modules

TL;DR

This paper investigates the structure and classification of extensions and irreducible modules over the Schr"odinger-Virasoro conformal algebra and its extension, providing new insights into their module theory.

Contribution

It classifies all finite nontrivial irreducible conformal modules and extensions over the Schr"odinger-Virasoro conformal algebra and its extension.

Findings

Classified all finite nontrivial irreducible modules

Determined extensions between modules over the algebra

Extended classification to Heisenberg-Virasoro conformal modules

Abstract

In this paper, we study extensions between two finite irreducible conformal modules over the Schr\"odinger-Virasoro conformal algebra and the extended Schr\"odinger-Virasoro conformal algebra. Also, we classify all finite nontrivial irreducible conformal modules over the extended Schr\"odinger-Virasoro conformal algebra. As a byproduct, we obtain a classification of extensions of Heisenberg-Virasoro conformal modules.