On the representation type of a finite tensor category
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914056197111808 |
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| author | Bergh, Petter Andreas Erdmann, Karin Plavnik, Julia Yael Witherspoon, Sarah |
| author_facet | Bergh, Petter Andreas Erdmann, Karin Plavnik, Julia Yael Witherspoon, Sarah |
| contents | Given an exact module category over a finite tensor category with finitely generated cohomology, we show that if there exists an object of complexity at least three, then the category is of wild representation type. In particular, if the Krull dimension of the cohomology ring of the finite tensor category is at least three, then this category is wild. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the representation type of a finite tensor category Bergh, Petter Andreas Erdmann, Karin Plavnik, Julia Yael Witherspoon, Sarah Quantum Algebra K-Theory and Homology Representation Theory 16G60, 16T05, 18M05, 18M15 Given an exact module category over a finite tensor category with finitely generated cohomology, we show that if there exists an object of complexity at least three, then the category is of wild representation type. In particular, if the Krull dimension of the cohomology ring of the finite tensor category is at least three, then this category is wild. |
| title | On the representation type of a finite tensor category |
| topic | Quantum Algebra K-Theory and Homology Representation Theory 16G60, 16T05, 18M05, 18M15 |
| url | https://arxiv.org/abs/2509.20853 |