Classification of Simple Cuspidal Modules over a Lattice Lie Algebra of Witt type

TL;DR

This paper classifies simple, uniformly bounded, ^N-graded modules over a lattice Lie algebra of Witt type, expanding understanding of module structures in this algebraic setting.

Contribution

It provides the first classification of simple ^N-graded modules with bounded multiplicities over the lattice Witt algebra.

Findings

Classified all simple modules with bounded multiplicities

Established criteria for module simplicity and grading

Extended module theory to lattice Witt type algebras

Abstract

Let $W_\pi$ be the lattice Lie algebra of Witt type associated with an additive inclusion $\pi: \mathbb{Z}^N \hookrightarrow \mathbb{C}^2$ with $N>1$. In this article, the classification of simple $\mathbb{Z}^N$-graded $W_\pi$-modules, whose multiplicities are uniformly bounded, is given.