# Classifying (Weak) Coideal Subalgebras of Weak Hopf C*-Algebras

## TL;DR

This paper introduces a general method for classifying weak coideal subalgebras within weak Hopf C*-algebras, exemplified through structures linked to Tambara Yamagami categories.

## Contribution

It provides a novel classification framework for weak coideal subalgebras in weak Hopf C*-algebras, with specific applications to Tambara Yamagami categories.

## Key findings

- Developed a general classification approach.
- Applied method to Tambara Yamagami categories.
- Enhanced understanding of subalgebra structures in weak Hopf C*-algebras.

## Abstract

We develop a general approach to the problem of classification of weak coideal C*-subalgebras of weak Hopf C*-algebras. As an example, we consider weak Hopf C*-algebras and their weak coideal C*-subalgebras associated with Tambara Yamagami categories.