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© 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.