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arXiv · 1504.03732

Abelian Tensors

J. M. Landsberg·Mateusz Michałek
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Abstract

We 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.

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J. M. Landsberg, Mateusz Michałek. 2015-04-14. Abelian Tensors. https://arxiv.org/abs/1504.03732

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