Finite-dimensional monomial algebras are determined by their automorphism group
Commutative Algebra
2026-05-13 v2 Algebraic Geometry
Rings and Algebras
Abstract
A monomial algebra is the quotient of a polynomial algebra by an ideal generated by monomials. We prove that finite-dimensional monomial algebras are characterized by their automorphism group among finite-dimensional, local algebras with cotangent space of fixed dimension. In particular, we show how to recover a monomial ideal given the automorphism group of the corresponding monomial algebra.
Cite
@article{arxiv.2409.15081,
title = {Finite-dimensional monomial algebras are determined by their automorphism group},
author = {Roberto Díaz and Giancarlo Lucchini Arteche},
journal= {arXiv preprint arXiv:2409.15081},
year = {2026}
}
Comments
12 pages, final version. Accepted for publication in Transformation Groups