Hilbert Function and Betti Numbers of Algebras with Lefschetz Property of Order m

TL;DR

This paper extends the characterization of Hilbert functions for algebras with the Lefschetz property to those with multiple Lefschetz properties, providing bounds for Betti numbers and conditions for their attainment.

Contribution

It generalizes existing results to algebras with the Lefschetz property m times and establishes upper bounds for Betti numbers in this context.

Findings

Extended Hilbert function characterization to m-times Lefschetz property

Derived upper bounds for Betti numbers of such algebras

Identified cases where bounds are achieved

Abstract

The authors T.Harima, J.C.Migliore, U.Nagel and J.Watanabe characterized the Hilbert function of algbebras with the Lefschetz property. We extend this characterization to algebras with the Lefschetz property m times. We also give upper bounds for the Betti numbers of Artinian algebras with a given Hilbert function and with the Lefschetz property m times and describe the cases in which these bounds are reached.