Whittaker modules for a Lie algebra of Block type

TL;DR

This paper explores Whittaker modules for a Lie algebra of Block type, establishing a correspondence between module classes and polynomial ring ideals, extending classical and Virasoro algebra results.

Contribution

It introduces a new framework for Whittaker modules in the context of Block type Lie algebras and generalizes existing classification results.

Findings

Established a one-to-one correspondence between isomorphism classes of Whittaker modules and polynomial ring ideals.

Extended classical Whittaker module classification to Block type Lie algebras.

Provided conditions under which the correspondence holds.

Abstract

In this paper, we study Whittaker modules for a Lie algebras of Block type. We define Whittaker modules and under some conditions, obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules over this algebra and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra.