A Note on Free Quantum Groups
- [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
Access Full Article
topAbstract
topHow to cite
topBanica, 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
top- T. Banica, Le groupe quantique compact libre U(n), Comm. Math. Phys. 190 (1997), 143-172 Zbl0906.17009MR1484551
- T. Banica, Representations of compact quantum groups and subfactors, J. Reine Angew. Math. 509 (1999), 167-198 Zbl0957.46038MR1679171
- T. Banica, J. Bichon, B. Collins, The hyperoctahedral quantum group, J. Ramanujan Math. Soc. 22 (2007), 345-384 Zbl1185.46046MR2376808
- T. Banica, B. Collins, Integration over compact quantum groups, Publ. Res. Inst. Math. Sci. 43 (2007), 377-302 Zbl1129.46058MR2341011
- A. Nica, R. Speicher, Lectures on the combinatorics of free probability, (2006), Cambridge University Press, Cambridge Zbl1133.60003MR2266879
- D.V. Voiculescu, Circular and semicircular systems and free product factors, Progress in Math. 92 (1990), 45-60 Zbl0744.46055MR1103585
- S. Wang, Free products of compact quantum groups, Comm. Math. Phys. 167 (1995), 671-692 Zbl0838.46057MR1316765
- S. Wang, Quantum symmetry groups of finite spaces, Comm. Math. Phys. 195 (1998), 195-211 Zbl1013.17008MR1637425
- S.L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665 Zbl0627.58034MR901157
- S.L. Woronowicz, Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93 (1988), 35-76 Zbl0664.58044MR943923
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.