A Note on Free Quantum Groups

Teodor Banica[1]

  • [1] Department of Mathematics Paul Sabatier University 118 route de Narbonne 31062 Toulouse, France

Annales mathématiques Blaise Pascal (2008)

  • Volume: 15, Issue: 2, page 135-146
  • ISSN: 1259-1734

Abstract

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We study the free complexification operation for compact quantum groups, G → G c . We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying G = G c .

How to cite

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Banica, Teodor. "A Note on Free Quantum Groups." Annales mathématiques Blaise Pascal 15.2 (2008): 135-146. <http://eudml.org/doc/10556>.

@article{Banica2008,
abstract = {We study the free complexification operation for compact quantum groups, $G\rightarrow G^c$. We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying $G=G^c$.},
affiliation = {Department of Mathematics Paul Sabatier University 118 route de Narbonne 31062 Toulouse, France},
author = {Banica, Teodor},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Free quantum group; free quantum group},
language = {eng},
month = {7},
number = {2},
pages = {135-146},
publisher = {Annales mathématiques Blaise Pascal},
title = {A Note on Free Quantum Groups},
url = {http://eudml.org/doc/10556},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Banica, Teodor
TI - A Note on Free Quantum Groups
JO - Annales mathématiques Blaise Pascal
DA - 2008/7//
PB - Annales mathématiques Blaise Pascal
VL - 15
IS - 2
SP - 135
EP - 146
AB - We study the free complexification operation for compact quantum groups, $G\rightarrow G^c$. We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying $G=G^c$.
LA - eng
KW - Free quantum group; free quantum group
UR - http://eudml.org/doc/10556
ER -

References

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  1. T. Banica, Le groupe quantique compact libre U(n), Comm. Math. Phys. 190 (1997), 143-172 Zbl0906.17009MR1484551
  2. T. Banica, Representations of compact quantum groups and subfactors, J. Reine Angew. Math. 509 (1999), 167-198 Zbl0957.46038MR1679171
  3. T. Banica, J. Bichon, B. Collins, The hyperoctahedral quantum group, J. Ramanujan Math. Soc. 22 (2007), 345-384 Zbl1185.46046MR2376808
  4. T. Banica, B. Collins, Integration over compact quantum groups, Publ. Res. Inst. Math. Sci. 43 (2007), 377-302 Zbl1129.46058MR2341011
  5. A. Nica, R. Speicher, Lectures on the combinatorics of free probability, (2006), Cambridge University Press, Cambridge Zbl1133.60003MR2266879
  6. D.V. Voiculescu, Circular and semicircular systems and free product factors, Progress in Math. 92 (1990), 45-60 Zbl0744.46055MR1103585
  7. S. Wang, Free products of compact quantum groups, Comm. Math. Phys. 167 (1995), 671-692 Zbl0838.46057MR1316765
  8. S. Wang, Quantum symmetry groups of finite spaces, Comm. Math. Phys. 195 (1998), 195-211 Zbl1013.17008MR1637425
  9. S.L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665 Zbl0627.58034MR901157
  10. S.L. Woronowicz, Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93 (1988), 35-76 Zbl0664.58044MR943923

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