# Stability of Lie group homomorphisms and Lie subgroups

## TL;DR

This paper investigates the stability of Lie group homomorphisms and subgroups under deformations, using a Moser type argument, with specific results for compact groups.

## Contribution

It introduces a Moser type argument to analyze the triviality of deformations of Lie group homomorphisms and subgroups, providing new stability results especially for compact groups.

## Key findings

- Deformations of Lie group homomorphisms can be trivialized under certain conditions.
- Stability results are established for compact Lie groups.
- The method extends to the study of Lie subgroups and their deformations.

## Abstract

We discuss a Moser type argument to show when a deformation of a Lie group homomorphism and of a Lie subgroup is trivial. For compact groups we obtain stability results.