On Partial Actions of Hopf-Ore Extensions

Source 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 $$g \cdot 1_R$$ g · 1 R is either $$1_R$$ 1 R or 0.