Hopf bimodules for bialgebroids
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911197182296064 |
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| author | Chemla, Sophie Kowalzig, Niels |
| author_facet | Chemla, Sophie Kowalzig, Niels |
| contents | Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Hopf modules, also known as Hopf bimodules or tetramodules, in this realm. By explicitly formulating a fundamental theorem for Hopf modules via the concept of Hopf-Galois comodules, we prove that the category of Hopf bimodules can be endowed with the structure of a (pre-)braided monoidal category in two different ways, which, in turn, are shown to be both braided monoidally equivalent to the category of Yetter-Drinfel'd modules, that is, to the monoidal centre of the category of left bialgebroid modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hopf bimodules for bialgebroids Chemla, Sophie Kowalzig, Niels Quantum Algebra Category Theory Rings and Algebras Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Hopf modules, also known as Hopf bimodules or tetramodules, in this realm. By explicitly formulating a fundamental theorem for Hopf modules via the concept of Hopf-Galois comodules, we prove that the category of Hopf bimodules can be endowed with the structure of a (pre-)braided monoidal category in two different ways, which, in turn, are shown to be both braided monoidally equivalent to the category of Yetter-Drinfel'd modules, that is, to the monoidal centre of the category of left bialgebroid modules. |
| title | Hopf bimodules for bialgebroids |
| topic | Quantum Algebra Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2510.06417 |