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- Title
The Full Classification of Orthogonal Easy Quantum Groups.
- Authors
Raum, Sven; Weber, Moritz
- Abstract
We study easy quantum groups, a combinatorial class of orthogonal quantum groups introduced by Banica-Speicher in 2009. We show that there is a countable descending chain of easy quantum groups interpolating between Bichon's free wreath product with the permutation group S and a semi-direct product of a permutation action of S on a free product. This reveals a series of new commutation relations interpolating between a free product construction and the tensor product. Furthermore, we prove a dichotomy result saying that every hyperoctahedral easy quantum group is either part of our new interpolating series of quantum groups or belongs to a class of semi-direct product quantum groups recently studied by the authors. This completes the classification of easy quantum groups. We also study combinatorial and operator algebraic aspects of the new interpolating series.
- Subjects
QUANTUM groups; COMMUTATION relations (Quantum mechanics); TENSOR products; OPERATOR algebras; CLASSIFICATION; PERMUTATION groups; MATHEMATICAL models
- Publication
Communications in Mathematical Physics, 2016, Vol 341, Issue 3, p751
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-015-2537-z