Biquadratic spaces of length two
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929651630211072 |
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| author | Danelon, Alessandro Snowden, Andrew |
| author_facet | Danelon, Alessandro Snowden, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Biquadratic spaces of length two Danelon, Alessandro Snowden, Andrew Representation Theory Logic 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. |
| title | Biquadratic spaces of length two |
| topic | Representation Theory Logic |
| url | https://arxiv.org/abs/2412.20681 |