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Hopf Images of Hopf algebra Coactions
Abstract
We introduce the Hopf image of a right coaction of a Hopf algebra on an algebra as the smallest Hopf subalgebra through which the coaction factors. We establish its basic properties and show that the induced coaction on the Hopf image is inner-faithful. For coactions on Nichols algebras arising from Yetter--Drinfeld modules, we prove that the Hopf image is the smallest Hopf subalgebra detected by the underlying coaction on the Yetter--Drinfeld module. We give explicit examples of proper non-trivial Hopf images arising from bosonizations.
Related
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BibTeX
@misc{bhattacharjee2026hopf,
title = {{Hopf Images of Hopf algebra Coactions}},
author = {Arnab Bhattacharjee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20118},
eprint = {2609.20118},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20118},
}
RIS
TY - UNPB
TI - Hopf Images of Hopf algebra Coactions
AU - Arnab Bhattacharjee
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20118
UR - https://arxiv.org/abs/2609.20118
AB - We introduce the Hopf image of a right coaction of a Hopf algebra on an algebra as the smallest Hopf subalgebra through which the coaction factors. We establish its basic properties and show that the induced coaction on the Hopf image is inner-faithful. For coactions on Nichols algebras arising from Yetter--Drinfeld modules, we prove that the Hopf image is the smallest Hopf subalgebra detected by the underlying coaction on the Yetter--Drinfeld module. We give explicit examples of proper non-trivial Hopf images arising from bosonizations.
ER -