New families of Artinian Gorenstein algebras with the weak Lefschetz property

TL;DR

This paper introduces new families of Artinian Gorenstein graded algebras with binomial Macaulay dual generators that satisfy the weak or strong Lefschetz property, expanding the known classes beyond codimension three.

Contribution

It constructs new families of Artinian Gorenstein algebras with binomial Macaulay dual generators in arbitrary codimension, demonstrating they satisfy the Lefschetz properties.

Findings

New families of algebras with the weak Lefschetz property

Algebras with the strong Lefschetz property in codimension three

Extension of known properties to arbitrary codimension

Abstract

We construct new families of Artinian Gorenstein graded $K$-algebras of arbitrary codimension having binomial Macaulay dual generators and satisfying the weak or the strong Lefschetz property. This is a companion paper to \cite{ADFMMSV}, which studies codimension three algebras having binomial Macaulay dual generators in great depth, establishing in particular that they enjoy the strong Lefschetz property.