# Cartan-Iwahori-Matsumoto decompositions for reductive groups

## TL;DR

This paper presents a concise and self-contained proof of the Cartan-Iwahori-Matsumoto decomposition for reductive groups, a fundamental structure in algebraic group theory.

## Contribution

It offers a simplified and self-contained argument establishing the existence of the decomposition, enhancing understanding and accessibility.

## Key findings

- Proves the existence of Cartan-Iwahori-Matsumoto decompositions for reductive groups
- Provides a simplified, self-contained proof
- Strengthens theoretical foundation in algebraic group theory

## Abstract

We provide a short and self-contained argument for the existence of Cartan-Iwahori-Matsumoto decompositions for reductive groups.