On decomposing monomial algebras with the Lefschetz properties

Abstract

We introduce a general technique for decomposing monomial algebras which we use to study the Lefschetz properties. We apply our technique to various classes of algebras, including monomial almost complete intersections and Gorenstein algebras. In particular, we prove that Gorenstein codimension three algebras arising from numerical semigroups have the strong Lefschetz property. We also study the reverse of the splitting operation -- a gluing operation -- which gives a way to construct monomial algebras with the Lefschetz properties.

Journal version 16 pages, 5 figures

References in corpus (2)

• The weak Lefschetz property for Artinian Gorenstein algebras of codimension three
• The weak Lefschetz property of Gorenstein algebras of codimension three associated to the Apéry sets

Cited by in corpus (3)

• The weak Lefschetz property of Gorenstein algebras of codimension three associated to the Apéry sets
• Forcing the weak Lefschetz property for equigenerated monomial ideals
• A machine learning approach to commutative algebra: Distinguishing table vs non-table ideals