Globalization and the biactegory of partial modules

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 $M$.

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Journal
ArXiv.org
Published
2025-06-23
Primary Topic
Algebraic structures and combinatorial models
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article
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article

Globalization and the biactegory of partial modules

ArXiv.org
Algebraic structures and combinatorial models
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Globalization and the biactegory of partial modules

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Abstract

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 $M$.

ArXiv.org
Openalex Percentile: Top 44%
Algebraic structures and combinatorial models
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Globalization and the biactegory of partial modules · ArXiv.org (2025) | TGRS Research Map | TGRS