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Isomorphisms and fusion rules of orthogonal free quantum groups and their free complexifications

Author: Sven Raum
Journal: Proc. Amer. Math. Soc. 140 (2012), 3207-3218
MSC (2010): Primary 46L54
Published electronically: January 20, 2012
MathSciNet review: 2917093
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Abstract: We show that all orthogonal free quantum groups are isomorphic to variants of the free orthogonal Wang algebra, the hyperoctahedral quantum group or the quantum permutation group. We also obtain a description of their free complexification. In particular we complete the calculation of fusion rules of all orthogonal free quantum groups and their free complexifications.

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  • 1. Teodor Banica, The representation theory of the free $ O(n)$ compact quantum group (Théorie des représentations du groupe quantique compact libre $ O(n)$), C. R. Acad. Sci. 322 (1996), no. 3, 241-244 (French). MR 1378260 (97a:46108)
  • 2. -, The free compact quantum group $ U(n)$ (Le groupe quantique compact libre $ U(n)$), Commun. Math. Phys. 190 (1997), no. 1, 143-172 (French). MR 1484551 (99k:46095)
  • 3. -, Symmetries of a generic coaction, Math. Ann. 314 (1999), no. 4, 763-780 (English). MR 1709109 (2001g:46146)
  • 4. -, A note on free quantum groups (Une note sur les groupes quantiques libres), Ann. Math. Blaise Pascal 15 (2008), no. 2, 135-146 (English). MR 2468039 (2010f:46107)
  • 5. Teodor Banica and Roland Speicher, Liberation of orthogonal Lie groups, Adv. Math. 222 (2009), no. 4, 1461-1501 (English). MR 2554941 (2010j:46125)
  • 6. Teodor Banica and Roland Vergnioux, Fusion rules for quantum reflection groups, J. Noncommut. Geom. 3 (2009), no. 3, 327-359 (English). MR 2511633 (2010i:46109)
  • 7. Shuzhou Wang, Free products of compact quantum groups, Commun. Math. Phys. 167 (1995), no. 3, 671-692 (English). MR 1316765 (95k:46104)
  • 8. -, Quantum symmetry groups of finite spaces, Commun. Math. Phys. 195 (1998), no. 1, 195-211 (English). MR 1637425 (99h:58014)
  • 9. S.L. Woronowicz, A remark on compact matrix quantum groups, Lett. Math. Phys. 21 (1991), no. 1, 35-39 (English). MR 1088408 (92k:46097)

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Additional Information

Sven Raum
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium

Keywords: Quantum groups, fusion rules.
Received by editor(s): October 22, 2010
Received by editor(s) in revised form: March 28, 2011
Published electronically: January 20, 2012
Additional Notes: This research was partially supported by the Marie Curie Research Training Network Non-Commutative Geometry MRTN-CT-2006-031962 and by Katholieke Universiteit Leuven BOF research grant OT/08/032
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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