Support varieties for finite tensor categories: the tensor product property
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909217791672320 |
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| author | Bergh, Petter Andreas Plavnik, Julia Yael Witherspoon, Sarah |
| author_facet | Bergh, Petter Andreas Plavnik, Julia Yael Witherspoon, Sarah |
| contents | We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In particular, we show that the tensor product property holds for all objects in a symmetric finite tensor category over an algebraically closed field of characteristic zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16082 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Support varieties for finite tensor categories: the tensor product property Bergh, Petter Andreas Plavnik, Julia Yael Witherspoon, Sarah Quantum Algebra K-Theory and Homology Representation Theory 16E40, 16T05, 18M05, 18M15 We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In particular, we show that the tensor product property holds for all objects in a symmetric finite tensor category over an algebraically closed field of characteristic zero. |
| title | Support varieties for finite tensor categories: the tensor product property |
| topic | Quantum Algebra K-Theory and Homology Representation Theory 16E40, 16T05, 18M05, 18M15 |
| url | https://arxiv.org/abs/2306.16082 |