A remark on automorphisms of tensor spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913948494725120 |
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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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark on automorphisms of tensor spaces Danelon, Alessandro Snowden, Andrew Representation Theory 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. |
| title | A remark on automorphisms of tensor spaces |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2507.13521 |