The Automorphism groups of zero-dimensional monomial algebras
Algebraic Geometry
2026-04-28 v2
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.
Cite
@article{arxiv.2408.02197,
title = {The Automorphism groups of zero-dimensional monomial algebras},
author = {Roberto Díaz and Alvaro Liendo and Gonzalo Manzano-Flores and Andriy Regeta},
journal= {arXiv preprint arXiv:2408.02197},
year = {2026}
}
Comments
Revised version with new results on the component group of the automorphism group