# Weak Hopf algebra symmetries of C^\*-algebra inclusions

Source: [Weak Hopf algebra symmetries of C^\*-algebra inclusions](<https://www.sota2.com/research/paper/68fa1f8c7a2b558e2932a7ad>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T18:46:13.054Z

Authors: K. Szlachanyi

Published: 2000-12-31T18:07:32.000Z

## Abstract

After a summary on module algebra actions of C^\*-weak Hopf algebras we outline the proof of a reconstruction theorem stating that every finite index depth 2 inclusion N \< M of unital C^\*-algebras with finite dimensional centers is isomorphic to the invariant subalgebra inclusion M^A \< M with respect to a regular weak Hopf algebra action. The proof uses the language of C^\*-2-categories.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0101005>)

[PDF](<https://arxiv.org/pdf/math/0101005.pdf>)