The Automorphism groups of zero-dimensional monomial algebras

TL;DR

This paper characterizes the automorphism groups of zero-dimensional monomial algebras over fields of characteristic zero, using classification of locally nilpotent derivations, and extends results to semigroup algebras.

Contribution

It provides an explicit classification of automorphism groups for monomial algebras, generalizing to semigroup algebras beyond polynomial rings.

Findings

Automorphism groups explicitly classified for zero-dimensional monomial algebras.

Homogeneous locally nilpotent derivations characterized for these algebras.

Extension of results to broader class of semigroup algebras.

Abstract

A monomial algebra B is defined as a quotient of a polynomial ring by a monomial ideal, which is an ideal generated by a finite set of monomials. In this paper, we determine the automorphism group of a monomial algebra B, under the assumption that B is a finite-dimensional vector space over a field of characteristic zero. We achieve this by providing an explicit classification of the homogeneous locally nilpotent derivations of B. The main body of the paper addresses the more general case of semigroup algebras, with the polynomial ring being a particular case.