Panov's theorem for weak Hopf algebras

TL;DR

This paper extends Panov's theorem to Ore extensions over weak Hopf algebras, providing conditions for preserving the weak Hopf algebra structure and applying these results to connected groupoid algebras.

Contribution

It generalizes Panov's theorem from Hopf algebras to weak Hopf algebras, broadening the understanding of algebra extensions.

Findings

Extended Panov's theorem to weak Hopf algebras

Derived conditions for Ore extensions to maintain weak Hopf structure

Analyzed Ore extensions of connected groupoid algebras

Abstract

Panov proved necessary and sufficient conditions to extend the Hopf algebra structure of an algebra $R$ to an Ore extension $R[x;\sigma,\delta]$ 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.