Irreducible Highest Weight Representations Of The Simple n-Lie Algebra

TL;DR

This paper classifies all irreducible highest weight modules, including infinite-dimensional ones, for the simple n-Lie algebra, and determines its primitive ideals, extending previous finite-dimensional classifications.

Contribution

It provides a complete classification of all irreducible highest weight modules for the simple n-Lie algebra, including infinite-dimensional cases, using a new approach.

Findings

Complete classification of irreducible highest weight modules.

Identification of all primitive ideals of the universal enveloping algebra.

Extension of finite-dimensional classification to infinite-dimensional modules.

Abstract

A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the infinite-dimensional ones. As a corollary we find all primitive ideals of the universal enveloping algebra of this simple n-Lie algebra.