This work demonstrates how to extend partial actions of Hopf algebras on algebras, highlighting specific cases and implications.
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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Silva et al. (2026) studied this question.
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