An Infinite Dimensional Approach to the Third Fundamental Theorem of Lie

TL;DR

This paper explores the third fundamental theorem of Lie within the framework of infinite dimensional matrices, offering a novel perspective on classical Lie theory.

Contribution

It introduces an infinite dimensional approach to Lie III, extending classical results to a broader mathematical setting.

Findings

Reformulation of Lie III using infinite dimensional matrices

New insights into the structure of Lie algebras

Potential applications in advanced algebra and geometry

Abstract

We revisit the third fundamental theorem of Lie (Lie III) for finite dimensional Lie algebras in the context of infinite dimensional matrices.