Tannaka-Krein reconstruction for coactions of finite quantum groupoids

TL;DR

This paper extends the Tannaka-Krein reconstruction theorem to coactions of finite quantum groupoids on unital C*-algebras, providing a new framework for understanding their structure.

Contribution

It introduces a Tannaka-Krein reconstruction theorem specifically for coactions of finite quantum groupoids on unital C*-algebras, a novel generalization.

Findings

Established the reconstruction theorem for finite quantum groupoid coactions

Provided a categorical framework for these coactions

Enhanced understanding of quantum symmetries in operator algebras

Abstract

We study coactions of finite quantum groupoids on unital $C^*$-algebras and obtain the Tannaka-Krein reconstruction theorem for them.