Globalization and the biactegory of partial modules
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909656744460288 |
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| author | Batista, Eliezer Hautekiet, William Vercruysse, Joost |
| author_facet | Batista, Eliezer Hautekiet, William Vercruysse, Joost |
| contents | We show that the category of partial modules over a Hopf algebra $H$ is a biactegory (a bimodule category) over the category of global $H$-modules. The corresponding enrichment of partial modules over global modules is described, and the close relation between the dilation of partial modules and Hom-objects arising from this enrichment is investigated. In particular, for finite-dimensional pointed Hopf algebras, the standard dilation of a partial module $M$ is isomorphic to the Hom-object from the monoidal unit to $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Globalization and the biactegory of partial modules Batista, Eliezer Hautekiet, William Vercruysse, Joost Rings and Algebras Category Theory Quantum Algebra Representation Theory 16T05, 18D20, 18D25 We show that the category of partial modules over a Hopf algebra $H$ is a biactegory (a bimodule category) over the category of global $H$-modules. The corresponding enrichment of partial modules over global modules is described, and the close relation between the dilation of partial modules and Hom-objects arising from this enrichment is investigated. In particular, for finite-dimensional pointed Hopf algebras, the standard dilation of a partial module $M$ is isomorphic to the Hom-object from the monoidal unit to $M$. |
| title | Globalization and the biactegory of partial modules |
| topic | Rings and Algebras Category Theory Quantum Algebra Representation Theory 16T05, 18D20, 18D25 |
| url | https://arxiv.org/abs/2506.18451 |