The Weak Lefschetz Property for Tensor Products of Artinian Monomial Algebras and Its Applications to Lollipop Graphs

TL;DR

This paper studies the weak Lefschetz property in tensor products of specific monomial algebras and applies the findings to classify this property for algebras associated with lollipop graphs.

Contribution

It introduces new classifications of the weak Lefschetz property for tensor products of Artinian monomial algebras and applies these results to graph-related algebraic structures.

Findings

Classified the weak Lefschetz property for algebras from lollipop graphs.

Established conditions under which tensor products of monomial algebras have the property.

Connected algebraic properties to combinatorial graph structures.

Abstract

In this paper, we investigate the weak Lefschetz property for tensor products of Artinian monomial algebras and complete quadratic monomial algebras. As an application, we classify the weak Lefschetz property of the Artinian algebras $A(L_{m,n})$, which are defined by the edge ideals of the lollipop graphs $L_{m,n}$ together with the squares of the variables.