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PreprintCC BY 4.0arXiv

One-dimensional partial actions of 8-dimensional Hopf algebras and right coideal subalgebras

  • Matheus Castelo
  • Leonardo Duarte Silva
  • William Hautekiet
  • Grasiela Martini
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Abstract

In this work, we complete the description of the one-dimensional partial actions of 8-dimensional Hopf algebras by computing the remaining cases: the Kac-Paljutkin algebra π’œ and the unique non-semisimple non-pointed Hopf algebra 𝒦. We prove that all these partial actions are symmetric, study their associated partial smash products and we determine all their partial coactions of dimension one. Beyond the 8-dimensional setting, we investigate which right coideal subalgebras of a Hopf algebra H can be realized as partial smash products underline Bbbk # H over the base field. In particular, we show that every right coideal subalgebra of a finite-dimensional cosemisimple Hopf algebra arises in this way.

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Cite

BibTeXRIS
BibTeX
@misc{castelo2026onedimensional,
  title = {{One-dimensional partial actions of 8-dimensional Hopf algebras and right coideal subalgebras}},
  author = {Matheus Castelo and Leonardo Duarte Silva and William Hautekiet and Grasiela Martini},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13502},
  eprint = {2609.13502},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13502},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - One-dimensional partial actions of 8-dimensional Hopf algebras and right coideal subalgebras
AU  - Matheus Castelo
AU  - Leonardo Duarte Silva
AU  - William Hautekiet
AU  - Grasiela Martini
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.13502
UR  - https://arxiv.org/abs/2609.13502
AB  - In this work, we complete the description of the one-dimensional partial actions of 8-dimensional Hopf algebras by computing the remaining cases: the Kac-Paljutkin algebra π’œ and the unique non-semisimple non-pointed Hopf algebra 𝒦. We prove that all these partial actions are symmetric, study their associated partial smash products and we determine all their partial coactions of dimension one. Beyond the 8-dimensional setting, we investigate which right coideal subalgebras of a Hopf algebra H can be realized as partial smash products underline Bbbk # H over the base field. In particular, we show that every right coideal subalgebra of a finite-dimensional cosemisimple Hopf algebra arises in this way.
ER  -