ARTINIAN GORENSTEIN ALGEBRAS THAT ARE FREE EXTENSIONS OVER k[t]/(tn), AND MACAULAY DUALITY

被引：1

作者：

Iarrobino, Anthony ^{[1
]}

Marques, Edrom Acias ^{[2
]}

McDaniel, Chris ^{[3
]}

机构：

[1] Northeastern Univ, Dept Math, Boston, MA 02115 USA

[2] Univ Evora, Ctr Invest Matemat & Aplicacoes, Dept Matemat, Evora, Portugal

[3] Endicott Coll, Dept Math, Beverly, MA USA

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2022年 / 14卷 / 04期

关键词：

Artinian algebra; free extension; Gorenstein algebra; Hilbert function; invariant; Lefschetz property; tensor product;

D O I：

10.1216/jca.2022.14.553

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

T. Harima and J. Watanabe studied the Lefschetz properties of free extension Artinian algebras C over a base A with fiber B. The free extensions are deformations of the usual tensor product; when C is also Gorenstein, so are A and B, and it is natural to ask for the relation among the Macaulay dual generators for the algebras. Writing a dual generator F for C as a homogeneous "polynomial" in T and the dual variables for B, and given the dual generator for B, we give sufficient conditions on F that ensure that C is a free extension of A = k[t]/(tn) with fiber B. We give examples exploring the sharpness of the statements. We also consider a special set of coinvariant algebras C which are free extensions of A, but which do not satisfy the sufficient conditions of our main result.

引用

页码：553 / 569

页数：17

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