Abelian tensors Academic Article uri icon


  • © 2016 Elsevier Masson SAS We analyze tensors in Cm⊗Cm⊗Cm 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(Cm) and the subvariety consisting of the Zariski closure of the variety of maximal tori, called the variety of reductions.

author list (cited authors)

  • Landsberg, J. M., & Michałek, M.

citation count

  • 10

publication date

  • September 2017