Finite Quantum Groupoids and Their Applications

TL;DR

This paper surveys the theory of finite quantum groupoids, highlighting their foundational aspects and diverse applications in areas like subfactors, quantum deformations, and topological invariants.

Contribution

It provides a comprehensive overview of finite quantum groupoids and explores their applications across multiple fields, consolidating existing knowledge.

Findings

Finite quantum groupoids underpin various structures in quantum algebra.

Applications include invariants of knots and 3-manifolds.

Connections to subfactor theory and quantum deformations are established.

Abstract

We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and 3-manifolds.