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

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.