The Differential and Functional Equations for a Lie Group Homomorphism are Equivalent

TL;DR

This paper proves that solving the functional equation for a Lie group homomorphism is equivalent to solving its associated differential equation, simplifying the process of finding such homomorphisms.

Contribution

It establishes the equivalence between the functional and differential equations for Lie group homomorphisms, clarifying a common but unproven assumption.

Findings

Functional equation solutions correspond to differential equation solutions

Simplifies the process of identifying Lie group homomorphisms

Provides a rigorous proof of a well-known folklore result

Abstract

I prove the "folklore" result that the functional equation for a Lie group homomorphism can be solved by solving the corresponding differential equation.