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arXiv · 2310.14368

The weak Lefschetz property of artinian algebras associated to paths and cycles

Hop D. Nguyen·Quang Hoa Tran
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Abstract

Given a base field $\Bbbk$ of characteristic zero, for each graph $G$, we associate the artinian algebra $A(G)$ defined by the edge ideal of $G$ and the squares of the variables. We study the weak Lefschetz property of $A(G)$. We classify some classes of graphs with relatively few edges, including paths and cycles, such that its associated artinian ring has the weak Lefschetz property.

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Hop D. Nguyen, Quang Hoa Tran. 2023-10-22. The weak Lefschetz property of artinian algebras associated to paths and cycles. https://arxiv.org/abs/2310.14368

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