Tensor spaces and the geometry of polynomial representations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911969599029248 |
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| author | Harman, Nate Snowden, Andrew |
| author_facet | Harman, Nate Snowden, Andrew |
| contents | A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we generalize that result: we show that each Zariski class of tensor spaces contains a weakly homogeneous space, which is unique up to isomorphism; here, we say that two tensor spaces are "Zariski equivalent" if they satisfy the same polynomial identities. Our work relies on the theory of $\mathbf{GL}$-varieties developed by Bik, Draisma, Eggermont, and Snowden. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor spaces and the geometry of polynomial representations Harman, Nate Snowden, Andrew Representation Theory Algebraic Geometry Logic A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we generalize that result: we show that each Zariski class of tensor spaces contains a weakly homogeneous space, which is unique up to isomorphism; here, we say that two tensor spaces are "Zariski equivalent" if they satisfy the same polynomial identities. Our work relies on the theory of $\mathbf{GL}$-varieties developed by Bik, Draisma, Eggermont, and Snowden. |
| title | Tensor spaces and the geometry of polynomial representations |
| topic | Representation Theory Algebraic Geometry Logic |
| url | https://arxiv.org/abs/2407.19132 |