English

Globalization and the biactegory of partial modules

Rings and Algebras 2025-06-24 v1 Category Theory Quantum Algebra Representation Theory

Abstract

We show that the category of partial modules over a Hopf algebra HH is a biactegory (a bimodule category) over the category of global HH-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 MM is isomorphic to the Hom-object from the monoidal unit to MM.

Keywords

Cite

@article{arxiv.2506.18451,
  title  = {Globalization and the biactegory of partial modules},
  author = {Eliezer Batista and William Hautekiet and Joost Vercruysse},
  journal= {arXiv preprint arXiv:2506.18451},
  year   = {2025}
}

Comments

34 pages, comments welcome

R2 v1 2026-07-01T03:29:06.509Z