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26 April 2024
 
  » arxiv » 1504.3732

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Abelian Tensors
J.M. Landsberg ; Mateusz Michałek ;
Date 14 Apr 2015
AbstractWe analyze tensors in the tensor product of three m-dimensional vector spaces 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 the space of endomorphisms of an m-dimensional vector space, and the subvariety consisting of the Zariski closure of the variety of maximal tori, called the variety of reductions.
Source arXiv, 1504.3732
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