Commutative exact algebras and modular tensor categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908729122750464 |
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| author | Shimizu, Kenichi Yadav, Harshit |
| author_facet | Shimizu, Kenichi Yadav, Harshit |
| contents | Inspired by the study of vertex operator algebra extensions, we answer the question of when the category of local modules over a commutative exact algebra in a braided finite tensor category is a (non-semisimple) modular tensor category. Along the way we provide sufficient conditions for the category of local modules to be rigid, pivotal and ribbon. We also discuss two ways to construct such commutative exact algebras. The first is the class of simple current algebras and the second is using right adjoints of central tensor functors. Furthermore, we discuss Witt equivalence and its relation with extensions of VOAs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Commutative exact algebras and modular tensor categories Shimizu, Kenichi Yadav, Harshit Quantum Algebra Category Theory Representation Theory Inspired by the study of vertex operator algebra extensions, we answer the question of when the category of local modules over a commutative exact algebra in a braided finite tensor category is a (non-semisimple) modular tensor category. Along the way we provide sufficient conditions for the category of local modules to be rigid, pivotal and ribbon. We also discuss two ways to construct such commutative exact algebras. The first is the class of simple current algebras and the second is using right adjoints of central tensor functors. Furthermore, we discuss Witt equivalence and its relation with extensions of VOAs. |
| title | Commutative exact algebras and modular tensor categories |
| topic | Quantum Algebra Category Theory Representation Theory |
| url | https://arxiv.org/abs/2408.06314 |