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arXiv · 2408.02197

The Automorphism groups of zero-dimensional monomial algebras

Roberto Díaz·Alvaro Liendo·Gonzalo Manzano-Flores·Andriy Regeta
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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.

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Roberto Díaz, Alvaro Liendo, Gonzalo Manzano-Flores, Andriy Regeta. 2026-09-14. The Automorphism groups of zero-dimensional monomial algebras. https://arxiv.org/abs/2408.02197

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