Affine algebraic monoids as endomorphisms' monoids of finite-dimensional algebras

TL;DR

This paper demonstrates that every affine algebraic monoid can be realized as the monoid of endomorphisms of some finite-dimensional algebra, expanding understanding of algebraic monoids and their representations.

Contribution

It establishes a universal construction linking affine algebraic monoids to endomorphism monoids of finite-dimensional algebras, including nonassociative cases.

Findings

Any affine algebraic monoid can be represented as an endomorphism monoid of a finite-dimensional algebra.

The construction applies to nonassociative algebras.

This bridges the gap between abstract algebraic monoids and concrete algebraic structures.

Abstract

In this note we prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.