Finite-dimensional monomial algebras are determined by their automorphism group

Roberto Díaz; Giancarlo Lucchini Arteche

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arXiv · 2409.15081

Finite-dimensional monomial algebras are determined by their automorphism group

Roberto Díaz·Giancarlo Lucchini Arteche

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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.

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Roberto Díaz, Giancarlo Lucchini Arteche. 2024-09-23. Finite-dimensional monomial algebras are determined by their automorphism group. https://arxiv.org/abs/2409.15081

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