A self-contained proof of the Artin-Wedderburn theorem in the case of finite-dimensional Von Neumann algebras

TL;DR

This paper offers a fully constructive, self-contained proof of the Artin-Wedderburn theorem specifically for finite-dimensional Von Neumann algebras, utilizing only fundamental linear algebra concepts.

Contribution

It provides a new, elementary proof of the theorem that is accessible without advanced functional analysis tools.

Findings

Proof is fully constructive and self-contained.

Uses only basic linear algebra notions.

Applicable to finite-dimensional Von Neumann algebras.

Abstract

We provide a self-contained proof of the Artin-Wedderburn theorem in the case of finite-dimensional Von Neumann algebras (or equivalently unital C* algebras) that is fully constructive and uses only basic notions of linear algebra.