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Biquadratic spaces of length two

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arxiv 2412.20681 v1 pith:47LK3YQX submitted 2024-12-30 math.RT math.LO

Alessandro Danelon , Andrew Snowden This is my paper · ORCID
classification math.RTmath.LO
keywords lengthspacestensorspacebiquadraticclassifyfinitehighly
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A remark on automorphisms of tensor spaces

    math.RT 2025-07 accept novelty 7.0 of 10

    Any graph automorphism group is realized as the automorphism group of a symmetric (3,2,2)-tensor space, and the paper constructs spaces where V is irreducible but V⊗2 has infinite length.

  2. The fundamental theorems of invariant theory for linearly oligomorphic groups

    math.RT 2026-07 accept novelty 6.0 of 10

    The G-invariant symmetric forms on V^m for the automorphism group G of a universal homogeneous λ-space are freely generated by the contractions of the defining forms with Schur functors on k^m.

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