Finite-dimensional monomial algebras are determined by their automorphism group
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917481216475136 |
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| author | Díaz, Roberto Arteche, Giancarlo Lucchini |
| author_facet | Díaz, Roberto Arteche, Giancarlo Lucchini |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15081 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite-dimensional monomial algebras are determined by their automorphism group Díaz, Roberto Arteche, Giancarlo Lucchini Commutative Algebra Algebraic Geometry Rings and Algebras 13F55, 16W20, 16W25, 13H99, 13N15, 52B20 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. |
| title | Finite-dimensional monomial algebras are determined by their automorphism group |
| topic | Commutative Algebra Algebraic Geometry Rings and Algebras 13F55, 16W20, 16W25, 13H99, 13N15, 52B20 |
| url | https://arxiv.org/abs/2409.15081 |