On Partial Actions of Hopf-Ore Extensions

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 $$g \cdot 1_R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>·</mml:mo> <mml:msub> <mml:mn>1</mml:mn> <mml:mi>R</mml:mi> </mml:msub> </mml:mrow> </mml:math> is either $$1_R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mn>1</mml:mn> <mml:mi>R</mml:mi> </mml:msub> </mml:math> or 0.