Winter 2022 Artinian Gorenstein algebras that are free extensions over k[t]/(tn), and Macaulay duality
Anthony Iarrobino, Pedro Macias Marques, Chris McDaniel
J. Commut. Algebra 14(4): 553-569 (Winter 2022). DOI: 10.1216/jca.2022.14.553


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.


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Anthony Iarrobino. Pedro Macias Marques. Chris McDaniel. "Artinian Gorenstein algebras that are free extensions over k[t]/(tn), and Macaulay duality." J. Commut. Algebra 14 (4) 553 - 569, Winter 2022.


Received: 18 July 2018; Revised: 13 August 2019; Accepted: 16 August 2019; Published: Winter 2022
First available in Project Euclid: 15 November 2022

MathSciNet: MR4509407
zbMATH: 1509.13025
Digital Object Identifier: 10.1216/jca.2022.14.553

Primary: 13A50 , 13D40 , 13E10 , 13H10 , 14D06

Keywords: artinian algebra , free extension , Gorenstein algebra , Hilbert function , invariant , Lefschetz property , tensor product

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium


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Vol.14 • No. 4 • Winter 2022
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