Biquadratic spaces of length two
Representation Theory
2024-12-31 v1 Logic
Abstract
A tensor space is a vector space equipped with a finite collection of multilinear forms. The length of a tensor space is its length as a representation of its symmetry group. Infinite dimension tensor spaces of finite length are special, highly symmetrical objects. We classify the (universal) biquadratic spaces of length two; there are seven families of them. As a corollary, we establish some cases of the linear analog of the Ryll-Nardzewski theorem. We view this work as a first attempt to classify highly symmetrical tensor spaces.
Cite
@article{arxiv.2412.20681,
title = {Biquadratic spaces of length two},
author = {Alessandro Danelon and Andrew Snowden},
journal= {arXiv preprint arXiv:2412.20681},
year = {2024}
}
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26 pages