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arXiv · 2507.13521

A remark on automorphisms of tensor spaces

Alessandro Danelon·Andrew Snowden
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Abstract

A tensor space is a vector space equipped with a finite collection of multi-linear forms. In recent years, a rich theory of infinite dimensional tensor spaces has emerged. In this note, we show that a large class of permutation groups can occur as the automorphism groups of such tensor spaces. Using this, we show that a tensor space can behave somewhat pathologically as a representation of its automorphism group.

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Alessandro Danelon, Andrew Snowden. 2025-07-17. A remark on automorphisms of tensor spaces. https://arxiv.org/abs/2507.13521

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