k-Lefschetz properties, sectional matrices and hyperplane arrangements

Elisa Palezzato; Michele Torielli

doi:10.1016/j.jalgebra.2021.10.014

k-Lefschetz properties, sectional matrices and hyperplane arrangements

Elisa Palezzato, Michele Torielli

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this article, we study the k-Lefschetz properties for non-Artinian algebras, proving that several known results in the Artinian case can be generalized in this setting. Moreover, we describe how to characterize the graded algebras having the k-Lefschetz properties using sectional matrices. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements, with particular attention to the class of free arrangements.

Original language	English (US)
Pages (from-to)	215-233
Number of pages	19
Journal	Journal of Algebra
Volume	590
DOIs	https://doi.org/10.1016/j.jalgebra.2021.10.014
State	Published - Jan 15 2022
Externally published	Yes

Keywords

Almost revlex ideals
Hyperplane arrangements
Lefschetz properties
Sectional matrices

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2021.10.014

Cite this

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abstract = "In this article, we study the k-Lefschetz properties for non-Artinian algebras, proving that several known results in the Artinian case can be generalized in this setting. Moreover, we describe how to characterize the graded algebras having the k-Lefschetz properties using sectional matrices. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements, with particular attention to the class of free arrangements.",

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author = "Elisa Palezzato and Michele Torielli",

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AU - Torielli, Michele

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N2 - In this article, we study the k-Lefschetz properties for non-Artinian algebras, proving that several known results in the Artinian case can be generalized in this setting. Moreover, we describe how to characterize the graded algebras having the k-Lefschetz properties using sectional matrices. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements, with particular attention to the class of free arrangements.

AB - In this article, we study the k-Lefschetz properties for non-Artinian algebras, proving that several known results in the Artinian case can be generalized in this setting. Moreover, we describe how to characterize the graded algebras having the k-Lefschetz properties using sectional matrices. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements, with particular attention to the class of free arrangements.

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KW - Hyperplane arrangements

KW - Lefschetz properties

KW - Sectional matrices

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

k-Lefschetz properties, sectional matrices and hyperplane arrangements

Abstract

Keywords

ASJC Scopus subject areas

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