An approach to annihilators in the context of vector field Lie algebras
Authors: Charles H. Conley, William Goode
Publication: Expositiones Mathematicae (2024)
arXiv: 2403.01728
MSC Classification: 17B66
Abstract
We present a general method for describing the annihilators of modules of Lie algebras under certain conditions, which hold for some tensor modules of vector field Lie algebras. As an example, we apply the method to obtain an efficient proof of previously known results on the annihilators of the bounded irreducible modules of Vec(ℝ).
Overview
This paper presents a method for describing annihilators of modules of Lie algebras under conditions that hold for tensor modules of vector field Lie algebras. We apply the method to obtain an efficient proof of known results on annihilators of bounded irreducible modules of Vec(ℝ).
The annihilator of a module determines its structure and relationships to other modules. Vector field Lie algebras are infinite-dimensional Lie algebras with applications in differential equations and mathematical physics. While bounded irreducible modules of Vec(ℝ) were previously classified, understanding their annihilators required case-by-case analysis. This work provides a systematic approach.