Nondegenerate module categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915150021263360 |
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| author | Walton, Chelsea Yadav, Harshit |
| author_facet | Walton, Chelsea Yadav, Harshit |
| contents | Due to the work of Shimizu (2019), various nondegeneracy conditions for braided finite tensor categories are equivalent. This theory is partially extended to braided module categories here. We introduce when a braided module category is "nondegenerate" and "factorizable", and establish that these properties are equivalent. The proof involves a new monadicity result for module categories. Lastly, we examine the Hopf case, using Kolb's (2020) notion of a quasitriangular comodule algebra to introduce "factorizable" comodule algebras. We then show that the representation category of a quasitriangular comodule algebra is nondegenerate in our sense precisely when the comodule algebra is factorizable. Several examples are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nondegenerate module categories Walton, Chelsea Yadav, Harshit Quantum Algebra Category Theory Representation Theory 18M15, 16T05 Due to the work of Shimizu (2019), various nondegeneracy conditions for braided finite tensor categories are equivalent. This theory is partially extended to braided module categories here. We introduce when a braided module category is "nondegenerate" and "factorizable", and establish that these properties are equivalent. The proof involves a new monadicity result for module categories. Lastly, we examine the Hopf case, using Kolb's (2020) notion of a quasitriangular comodule algebra to introduce "factorizable" comodule algebras. We then show that the representation category of a quasitriangular comodule algebra is nondegenerate in our sense precisely when the comodule algebra is factorizable. Several examples are provided. |
| title | Nondegenerate module categories |
| topic | Quantum Algebra Category Theory Representation Theory 18M15, 16T05 |
| url | https://arxiv.org/abs/2411.18453 |