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Partial coactions of Hopf algebras on nonunital algebras and categories
Abstract
In this paper, we introduce and investigate partial coactions of a Hopf algebra on an associative, possibly nonunital algebra and on Bbbk-linear categories. We prove that every partial coaction has a globalization in a broad sense. We study in detail the case of a partial coaction on an algebra with local units; we prove that such a coaction is always induced from a global coaction, and we show that there exists a naturally associated Bbbk-linear category endowed with a partial coaction.
Related
- Coactions of weak multiplier Hopf algebras
- Frobenius functors and one-sided Hopf algebras in braided monoidal categories
- Exact sequences of representation categories of weak Hopf algebras
- One-dimensional partial actions of 8-dimensional Hopf algebras and right coideal subalgebras
- Hopf Images of Hopf algebra Coactions
BibTeX
@misc{alves2026partial,
title = {{Partial coactions of Hopf algebras on nonunital algebras and categories}},
author = {Marcelo Muniz Alves and Tiago Luiz Ferrazza},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01231},
eprint = {2611.01231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01231},
}
RIS
TY - UNPB
TI - Partial coactions of Hopf algebras on nonunital algebras and categories
AU - Marcelo Muniz Alves
AU - Tiago Luiz Ferrazza
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01231
UR - https://arxiv.org/abs/2611.01231
AB - In this paper, we introduce and investigate partial coactions of a Hopf algebra on an associative, possibly nonunital algebra and on Bbbk-linear categories. We prove that every partial coaction has a globalization in a broad sense. We study in detail the case of a partial coaction on an algebra with local units; we prove that such a coaction is always induced from a global coaction, and we show that there exists a naturally associated Bbbk-linear category endowed with a partial coaction.
ER -