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2016 Elsevier Masson SAS We analyze tensors in CmCmCm satisfying Strassen's equations for border rank m. Results include: two purely geometric characterizations of the CoppersmithWinograd 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.
Journal de Mathmatiques Pures et Appliques
author list (cited authors)
Landsberg, J. M., & Michaek, M.
complete list of authors
Landsberg, JM||Michałek, Mateusz