On the classification of easy quantum groups

By Moritz Weber. 2012

67 citations recorded by the source corpus.

Abstract In 2009, Banica and Speicher began to study the compact quantum groups G with S n ⊆ G ⊆ O n + whose intertwiner spaces are induced by some partitions. These so-called easy quantum groups have a deep connection to combinatorics. We continue their work on classifying these objects, by introducing some new examples of easy quantum groups. In particular, we show that the six easy groups O n , S n , H n , B n , S n ′ and B n ′ split into seven cases O n + , S n + , H n + , B n + , S n ′ + , B n ′ + and B n # + on the side of free easy quantum groups. Also, we give a complete classification in the half-liberated and in the nonhyperoctahedral case.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1f3c0bfd083078ab7299239473a7a207cff6b4b6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Moritz Weber
2. Sven Raum
3. Roland Speicher
4. Amaury Freslon

In Mathematical Physics

1. Moritz Weber
2. Sven Raum
3. Roland Speicher
4. Amaury Freslon
5. Pierre Tarrago

In Statistics and Probability

1. Sven Raum
2. Moritz Weber
3. Roland Speicher

Citations in the corpus

• The Full Classification of Orthogonal Easy Quantum Groups (2013, methodology): “It began in [BaSp09], and was continued in [BaCuSp10], [We13],[RaWe13a] and [RaWe13b].”
• Free Probability and Random Matrices (2014, background): “This has triggered quite some investigations on more general quantum symmetries and its relations to de Finetti theorems, see [4, 5, 32, 52].”