Abelian tensors

J. M. Landsberg*, Mateusz Michalek

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We analyze tensors in C-m circle times C-m circle times C-m satisfying Strassen's equations for border rank m. Results include: two purely geometric characterizations of the Coppersmith Winograd tensor, a reduction to the study of symmetric tensors under a mild genericity hypothesis, and numerous additional equations and examples. This study is closely connected to the study of the variety of m-dimensional abelian subspaces of End(C-m) and the subvariety consisting of the Zariski closure of the variety of maximal tori, called the variety of reductions. (C) 2016 Elsevier Masson SAS. All rights reserved.

Original languageEnglish
Pages (from-to)333-371
Number of pages39
JournalJOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume108
Issue number3
DOIs
Publication statusPublished - Sep 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Tensor
  • Commuting matrices
  • Strassen's equations
  • DIRECT SUM CONJECTURE
  • MATRIX MULTIPLICATION
  • SECANT VARIETIES
  • RANK
  • BOUNDS

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