The strong Lefschetz property and simple extensions

TL;DR

This paper demonstrates that the strong Lefschetz property is preserved under simple extensions of Artinian Gorenstein algebras, expanding the class of algebras known to possess this property.

Contribution

It proves that simple extensions of Artinian Gorenstein algebras with the strong Lefschetz property also have it, generalizing previous results on monomial complete intersections.

Findings

Simple extensions preserve the strong Lefschetz property.

Extension of monomial complete intersections retains the property.

Broadens understanding of algebraic structures with the strong Lefschetz property.

Abstract

Stanley showed that monomial complete intersections have the strong Lefschetz property. Extending this result we show that a simple extension of an Artinian Gorenstein algebra with the strong Lefschetz property has again the strong Lefschetz property.