A new proof of Stanley’s theorem on the strong Lefschetz property
Volume 173 / 2023
Colloquium Mathematicum 173 (2023), 1-8
MSC: Primary 13C40; Secondary 13E10, 14M10.
DOI: 10.4064/cm8987-11-2022
Published online: 24 January 2023
Abstract
A standard graded artinian monomial complete intersection algebra $A=\Bbbk [x_1,\ldots ,x_n]/(x_1^{a_1},\ldots ,x_n^{a_n})$, with $\Bbbk $ a field of characteristic zero, has the strong Lefschetz property defined by Stanley in 1980. In this paper, we give a new proof for this result by using only the basic linear algebra. Furthermore, our proof is still valid in the case where the characteristic of $\Bbbk $ is greater than the socle degree of $A$, namely $a_1+\cdots +a_n - n$.
