Communications in Mathematical Physics

, Volume 341, Issue 3, pp 751–779 | Cite as

The Full Classification of Orthogonal Easy Quantum Groups

Article

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 Sn and a semi-direct product of a permutation action of Sn 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.

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faktultät Mathematik und InformatikWestfälische Wilhelmsuniversität MünsterMünsterGermany
  2. 2.Fachbereich MathematikSaarland UniversitySaarbrückenGermany

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