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arXiv · 2609.13502

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 $\mathcal{A}$ and the unique non-semisimple non-pointed Hopf algebra $\mathcal{K}$. 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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Matheus Castelo, Leonardo Duarte Silva, William Hautekiet, Grasiela Martini. 2026-09-11. One-dimensional partial actions of 8-dimensional Hopf algebras and right coideal subalgebras. https://arxiv.org/abs/2609.13502

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