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Dostęp zamkniętyConcise tensors of minimal border rank
| cris.lastimport.scopus | 2024-02-12T19:55:12Z |
| dc.abstract.en | We determine defining equations for the set of concise tensors of minimal border rank in Cm ⊗Cm ⊗Cm when m = 5 and the set of concise minimal border rank 1∗-generic tensors when m = 5, 6. We solve the classical problem in algebraic complexity theory of classifying minimal border rank tensors in the special case m = 5. Our proofs utilize two recent developments: the 111-equations defined by Buczy´nska–Buczy´nski and results of Jelisiejew–Šivic on the variety of commuting matrices. We introduce a new algebraic invariant of a concise tensor, its 111-algebra, and exploit it to give a strengthening of Friedland’s normal form for 1-degenerate tensors satisfying Strassen’s equations. We use the 111-algebra to characterize wild minimal border rank tensors and classify them in C5⊗C5⊗C5 . |
| dc.affiliation | Uniwersytet Warszawski |
| dc.contributor.author | Pal, Arpan |
| dc.contributor.author | Landsberg, J. M. |
| dc.contributor.author | Jelisiejew, Joachim |
| dc.date.accessioned | 2024-01-24T20:05:49Z |
| dc.date.available | 2024-01-24T20:05:49Z |
| dc.date.issued | 2023 |
| dc.description.finance | Publikacja bezkosztowa |
| dc.identifier.doi | 10.1007/S00208-023-02569-Y |
| dc.identifier.issn | 0025-5831 |
| dc.identifier.uri | https://repozytorium.uw.edu.pl//handle/item/103505 |
| dc.identifier.weblink | https://link.springer.com/content/pdf/10.1007/s00208-023-02569-y.pdf |
| dc.language | eng |
| dc.pbn.affiliation | mathemathics |
| dc.relation.ispartof | Mathematische Annalen |
| dc.relation.pages | 1-45 |
| dc.rights | ClosedAccess |
| dc.sciencecloud | nosend |
| dc.title | Concise tensors of minimal border rank |
| dc.type | JournalArticle |
| dspace.entity.type | Publication |