Lefschetz Properties of Gorenstein Graded Algebras associated to the Ap\'ery Set of a Numerical Semigroup

TL;DR

This paper investigates the Weak Lefschetz property in specific Gorenstein graded algebras linked to the Apéry set of numerical semigroups, providing new transfer results for this property.

Contribution

It introduces a general transfer theorem for the Weak Lefschetz property from Gorenstein algebras to their quotients by colon ideals.

Findings

Established conditions for Weak Lefschetz property in the studied algebras.

Proved a transfer theorem for Weak Lefschetz property in Gorenstein algebras.

Applied results to classes of algebras associated with numerical semigroups.

Abstract

In this paper we study the Weak Lefschetz property of two classes of standard graded Artinian Gorenstein algebras associated in a natural way to the Ap\'ery set of numerical semigroups. To this aim we also prove a general result about the transfer of Weak Lefschetz property from an Artinian Gorenstein algebra to its quotients modulo a colon ideal.