Lefschetz properties of some codimension three Artinian Gorenstein algebras

Abdallah, Nancy (author): Högskolan i Borås,Akademin för textil, teknik och ekonomi

Altafi, Nasrin (author): KTH,Matematik (Inst.),Dept Math, S-10044 Stockholm, Sweden.;Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada.,Department of Mathematics, KTH Royal Institute of Technology, S-100 44 Stockholm, Sweden; Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, K7L 3N6, Canada

Iarrobino, Anthony (author): Northeastern Univ, Dept Math, Boston, MA 02115 USA.,Department of Mathematics, Northeastern University, Boston, MA 02115, USA

Seceleanu, Alexandra (author): Univ Nebraska Lincoln, Dept Math, Lincoln, NE 68588 USA.,Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, USA

Yameogo, Joachim (author): Univ Cote dAzur, CNRS, LJAD, Nice, France.,Université Côte d'Azur, CNRS, LJAD, France

(creator_code:org_t)

Elsevier BV, 2023
2023
English.
In: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 625, s. 28-45

Related links:: https://urn.kb.se/re...; show more...; https://doi.org/10.1...; https://urn.kb.se/re...; show less...

Abstract Subject headings

Codimension two Artinian algebras have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three Artinian Gorenstein algebras. Despite much work, the strong Lefschetz property for codimension three Artinian Gorenstein algebra has remained largely mysterious; our results build on and strengthen some of the previous results. We here show that every standard-graded codimension three Artinian Gorenstein algebra A having maximum value of the Hilbert function at most six has the strong Lefschetz property, provided that the characteristic is zero. When the characteristic is greater than the socle degree of A, we show that A is almost strong Lefschetz, they are strong Lefschetz except in the extremal pair of degrees.

By the author/editor: Abdallah, Nancy; Altafi, Nasrin; Iarrobino, Antho ...; Seceleanu, Alexa ...; Yameogo, Joachim

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Algebra and Logi ...

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