Panov’s theorem for weak Hopf algebras

Abstract

Panov proved necessary and sufficient conditions to extend the Hopf algebra structure of an algebra R to an Ore extension R[x; σ, δ] with x being a skew-primitive element. In this paper we extend Panov's result to Ore extensions over weak Hopf algebras. As an application we study Ore extensions of connected groupoid algebras.The first author is a member of CMUP (UID/MAT/00144/2013), which is funded by FCT with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020.