2024/12/30 by Alessandro Danelon, Danelon, Alessandro, Andrew Snowden +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Logic (math.LO) #Mathematics and Applications #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2412.20681
openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.