Finite-dimensional monomial algebras are determined by their automorphism group

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.

arXiv comment12 pages, final version. Accepted for publication in Transformation Groups