Finite Quantum Groupoids and Their Applications

2000/06/07 by Dmitri Nikshych, Nikshych, Dmitri, Leonid Vaînerman +2 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA

paper · pdf · doi:10.48550/arxiv.math/0006057

44 pages, amslatex

openalex publication_date 2000/06/07 · arxiv created 2000/06/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Duality for actions of weak Kac algebras and crossed product inclusions of II₁ factors
• Weak Hopf Algebras and Reducible Jones Inclusions of Depth 2. I: From Crossed products to Jones towers
• HOPF ALGEBROIDS AND QUANTUM GROUPOIDS
• Invariants of 3-manifolds via link polynomials and quantum groups

Cited by

• Quantum Cluster State Spin Chain with Ising Fusion Category Symmetry: A Perspective from Weak Hopf SymTFT

Related

• Invariants of Knots and 3-manifolds from Quantum Groupoids
• Finite quantum groupoids and inclusions of finite type
• Galois actions by finite quantum groupoids
• Algebraic Versions of a Finite-Dimensional Quantum Groupoid
• A Duality Theorem for Quantum Groupoids