Tannaka-Krein duality for compact quantum homogeneous spaces. II. Classification of quantum homogeneous spaces for quantum SU(2)

Abstract

We apply the Tannaka-Krein duality theory for quantum homogeneous spaces, developed in the first part of this series of papers, to the case of the quantum SU(2) groups. We obtain a classification of their quantum homogeneous spaces in terms of weighted oriented graphs. The equivariant maps between these quantum homogeneous spaces can be characterized by certain quadratic equations associated with the braiding on the representations of SUq(2). We show that, for |q| close to 1, all quantum homogeneous spaces are realized by coideals.

v2: improvements on graph norm bound and other minor modifications, 30 pages; v1: sequel to arXiv:1211.6552, 32 pages

Cited by in corpus (12)

• Operator algebras in rigid C*-tensor categories
• AdS Poisson homogeneous spaces and Drinfel'd doubles
• Partial compact quantum groups
• Quantum subgroups of the compact quantum group SU_{-1}(3)
• Ribbon braided module categories, quantum symmetric pairs and Knizhnik-Zamolodchikov equations
• Local topological order and boundary algebras
• Tensor category equivariant KK-theory
• Quantum graphs, subfactors and tensor categories I
• Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility
• Discrete Inclusions of C*-algebras
• Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories
• On fixed point planar algebras