On the problem of classifying simple compact quantum groups

Abstract

We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups. Several new quantum groups constructed by Banica, Curran and Speicher since the author's first paper on simple quantum groups are shown to be simple using results of Raum and Weber.

25 pages

References in corpus (4)

• A noncommutative de Finetti theorem: Invariance under quantum permutations is equivalent to freeness with amalgamation
• Faithful compact quantum group actions on connected compact metrizable spaces
• Quantum Group of Orientation preserving Riemannian Isometries
• Algebraic quantum permutation groups