Representations for the non-graded Virasoro-like algebra

TL;DR

This paper classifies irreducible modules over the non-graded Virasoro-like algebra, showing they are either GHW modules or uniformly bounded, and provides a classification for some uniformly bounded modules.

Contribution

It introduces a classification of irreducible modules over the non-graded Virasoro-like algebra, expanding understanding of their structure.

Findings

Irreducible modules are GHW or uniformly bounded.

Classification of some uniformly bounded modules is achieved.

Provides a natural condition under which modules are classified.

Abstract

It is proved that an irreducible module over the non-graded Virasoro-like algebra, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, the classification of some uniformly bounded modules is given.