no. 2
A Note on Free Quantum Groups
[Une Note sur les Groupes Quantiques Libres]
Banica, Teodor1
1 Department of Mathematics Paul Sabatier University 118 route de Narbonne 31062 Toulouse, France
Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 2, pp. 135-146.

On étudie l’opération de complexification libre pour les groupes quantiques compacts, G→G c . On montre qu’avec des définitions convenables, cette opération induit une bijection entre groupes quantiques orthogonaux libres de niveau infini, et groupes quantiques unitaires libres satisfaisant G=G c .

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 .

DOI : 10.5802/ambp.243
Classification : 16W30
Keywords: Free quantum group
Mot clés : Groupe quantique libre
Banica, Teodor 1

1 Department of Mathematics Paul Sabatier University 118 route de Narbonne 31062 Toulouse, France 
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Banica, Teodor. A Note on Free Quantum Groups. Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 2, pp. 135-146. doi : 10.5802/ambp.243. http://archive.numdam.org/articles/10.5802/ambp.243/

[1] Banica, T. Le groupe quantique compact libre U(n), Comm. Math. Phys., Volume 190 (1997), pp. 143-172 | DOI | MR | Zbl

[2] Banica, T. Representations of compact quantum groups and subfactors, J. Reine Angew. Math., Volume 509 (1999), pp. 167-198 | DOI | MR | Zbl

[3] Banica, T.; Bichon, J.; Collins, B. The hyperoctahedral quantum group, J. Ramanujan Math. Soc., Volume 22 (2007), pp. 345-384 | MR | Zbl

[4] Banica, T.; Collins, B. Integration over compact quantum groups, Publ. Res. Inst. Math. Sci., Volume 43 (2007), p. 377-302 | DOI | MR | Zbl

[5] Nica, A.; Speicher, R. Lectures on the combinatorics of free probability, Cambridge University Press, Cambridge, 2006 | MR | Zbl

[6] Voiculescu, D.V. Circular and semicircular systems and free product factors, Progress in Math., Volume 92 (1990), pp. 45-60 | MR | Zbl

[7] Wang, S. Free products of compact quantum groups, Comm. Math. Phys., Volume 167 (1995), pp. 671-692 | DOI | MR | Zbl

[8] Wang, S. Quantum symmetry groups of finite spaces, Comm. Math. Phys., Volume 195 (1998), pp. 195-211 | DOI | MR | Zbl

[9] Woronowicz, S.L. Compact matrix pseudogroups, Comm. Math. Phys., Volume 111 (1987), pp. 613-665 | DOI | MR | Zbl

[10] Woronowicz, S.L. Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math., Volume 93 (1988), pp. 35-76 | DOI | MR | Zbl

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