Ideals of general linear Lie algebras of infinite-dimensional vector spaces

TL;DR

This paper classifies the ideals of the Lie algebra of all linear transformations on an infinite-dimensional vector space over a field with characteristic not 2.

Contribution

It provides a complete classification of ideals in the Lie algebra gl(V) for infinite-dimensional vector spaces, extending understanding of their algebraic structure.

Findings

Complete classification of ideals of gl(V)

Extension of finite-dimensional Lie algebra results to infinite dimensions

Clarification of ideal structure over fields with characteristic not 2

Abstract

Let V be an infinite-dimensional vector space over a field of characteristic not equal to 2. We classify ideals of the Lie algebra gl(V) of all linear transformations of the space V.