What does this research mean for the field?

A partial action of a Hopf Algebra A on an algebra R can be extended to a partial action of a Hopf-Ore extension of A on R, enabling the characterization of all partial actions of rank one Hopf algebras under specific identity conditions. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to extend the understanding of how partial actions of Hopf algebras can be applied to Hopf-Ore extensions.

June 27, 2026Bulletin of the Brazilian Mathematical Society New Series0 citationsOpen Access

On Partial Actions of Hopf-Ore Extensions

LSLeonardo Duarte SilvaUniversidade Federal do Rio Grande do Sul JGJoão Matheus Jury GiraldiUniversidade Federal do Rio Grande do Sul GMGrasiela MartiniUniversidade Federal do Rio Grande do Sul

Key Points

This research aims to extend the understanding of how partial actions of Hopf algebras can be applied to Hopf-Ore extensions.
The study involves analyzing the extension of partial actions of a Hopf algebra A on an algebra R.
It specifically examines partial actions corresponding to rank one Hopf algebras, such as generalized Taft algebras and Radford algebras.
Mathematical conditions for the behavior of elements in the algebra R under these actions are explored.
Identified conditions under which the action of elements results in 1_R or 0 in the algebra R.
Classified the structure of all partial actions for rank one Hopf algebras on a given algebra R.

Abstract

Abstract In this work we study how to extend a partial action of a Hopf Algebra A on an algebra R to a partial action of a Hopf-Ore extension of A on R. As consequence, we exhibit all partial actions of rank one Hopf algebras (in particular, generalized Taft algebras and Radford algebras) on an algebra R for which g 1R g · 1 R is either 1R 1 R or 0.

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