Pivotality, twisted centres and the anti-double of a Hopf monad
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866917581552615424 |
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| author | Halbig, Sebastian Zorman, Tony |
| author_facet | Halbig, Sebastian Zorman, Tony |
| contents | Finite-dimensional Hopf algebras admit a correspondence between so-called pairs in involution, one-dimensional anti-Yetter--Drinfeld modules and algebra isomorphisms between the Drinfeld and anti-Drinfeld double. We extend it to general rigid monoidal categories and provide a monadic interpretation under the assumption that certain coends exist. Hereto we construct and study the anti-Drinfeld double of a Hopf monad. As an application the connection with the pivotality of Drinfeld centres and their underlying categories is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_05361 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pivotality, twisted centres and the anti-double of a Hopf monad Halbig, Sebastian Zorman, Tony Quantum Algebra Category Theory primary:18M15, secondary: 16T05, 18C20, 18M30 Finite-dimensional Hopf algebras admit a correspondence between so-called pairs in involution, one-dimensional anti-Yetter--Drinfeld modules and algebra isomorphisms between the Drinfeld and anti-Drinfeld double. We extend it to general rigid monoidal categories and provide a monadic interpretation under the assumption that certain coends exist. Hereto we construct and study the anti-Drinfeld double of a Hopf monad. As an application the connection with the pivotality of Drinfeld centres and their underlying categories is discussed. |
| title | Pivotality, twisted centres and the anti-double of a Hopf monad |
| topic | Quantum Algebra Category Theory primary:18M15, secondary: 16T05, 18C20, 18M30 |
| url | https://arxiv.org/abs/2201.05361 |