Classification of Finite Potent Endomorphisms

TL;DR

This paper introduces a new family of invariants to classify finite potent endomorphisms on arbitrary vector spaces, extending classical finite-dimensional classifications to infinite-dimensional cases, including nilpotent endomorphisms.

Contribution

It generalizes the classification of endomorphisms from finite-dimensional to infinite-dimensional vector spaces using novel invariants.

Findings

Developed a family of invariants for classification

Extended classification to infinite-dimensional spaces

Classified nilpotent endomorphisms in this broader context

Abstract

The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular case we classify nilpotent endomorphisms on infinite-dimensional vector spaces.