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Jordan types with small parts for Artinian Gorenstein algebras of codimension three
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1592-8915
2022 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 646, p. 54-83Article in journal (Refereed) Published
Abstract [en]

We study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that represent the ranks of multiplication maps in various degrees. We show that there is a 1-1 correspondence between rank matrices and Jordan degree types. For Artinian Gorenstein algebras with codimension three we classify all rank matrices that occur for linear forms with vanishing third power. As a consequence, we show for such algebras that the possible Jordan types with parts of length at most four are uniquely determined by at most three parameters.

Place, publisher, year, edition, pages
Elsevier BV , 2022. Vol. 646, p. 54-83
Keywords [en]
Artinian Gorenstein algebra, Hilbert function, Catalecticant matriz, Hessians, Macaulay dual generators, Jordan type, Partition
National Category
Physical Geography Other Mathematics Algebra and Logic
Identifiers
URN: urn:nbn:se:kth:diva-314824DOI: 10.1016/j.laa.2022.03.013ISI: 000806382200004Scopus ID: 2-s2.0-85127237679OAI: oai:DiVA.org:kth-314824DiVA, id: diva2:1676894
Note

QC 20220627

Available from: 2022-06-27 Created: 2022-06-27 Last updated: 2022-06-27Bibliographically approved

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Altafi, Nasrin

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