A new proof of Stanley's theorem on the strong Lefschetz property

2022/11/24 by Phuong, Ho V. N., Tran, Quang Hoa · 1 citation
#13C40 #13E10 #14M10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.13548

Abstract

A standard graded artinian monomial complete intersection algebra A=\Bbbk[x₁,x₂,…,x_n]/(x₁^a₁,x₂^a₂,…,x_n^a_n), with \Bbbk a field of characteristic zero, has the strong Lefschetz property due to Stanley in 1980. In this paper, we give a new proof for this result by using only the basic properties of linear algebra. Furthermore, our proof is still true in the case where the characteristic of \Bbbk is greater than the socle degree of A, namely a₁+a₂+⋯+a_n - n.

Cited by

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

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