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Growth rates of dimensional invariants of compact quantum groups and a theorem of Høegh-Krohn, Landstad and Størmer
Author:
Claudia Pinzari
Journal:
Proc. Amer. Math. Soc. 141 (2013), 895-907
MSC (2010):
Primary 46L55, 46L65; Secondary 37A55, 28D20
Posted:
July 5, 2012
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Additional Information
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- 1.
- T. Banica: Le groupe quantique compact libre
. Comm. Math. Phys., 190 (1997), 143-172. MR 1484551 (99k:46095)
- 2.
- J. Bichon, A. De Rijdt, S. Vaes: Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups. Comm. Math. Phys., 262 (2006), 703-728. MR 2202309 (2007a:46072)
- 3.
- F.P. Boca: Ergodic actions of compact matrix pseudogroups on
-algebras. In: Recent advances in operator algebras (Orléans, 1992). Astérisque, 232 (1995), 93-109. MR 1372527 (97d:46075)
- 4.
- A. Connes: Une classification des facteurs de type
. Ann. Sci. École Norm. Sup., 6 (1973), 133-252. MR 0341115 (49:5865)
- 5.
- A. Connes: Almost periodic states and factors of type
. J. Funct. Analysis, 16 (1974), 415-445. MR 0358374 (50:10840)
- 6.
- S. Doplicher, R. Longo, J.E. Roberts, L. Zsido: A remark on quantum group actions and nuclearity. Rev. Math. Phys., 14 (2002), 787-796. MR 1932666 (2003h:46097)
- 7.
- R. Høegh-Krohn, M.B. Landstad, E. Størmer: Compact ergodic groups of automorphisms, Ann. of Math. (2), 114 (1981), 75-86. MR 625345 (82i:46097)
- 8.
- R. Longo, J.E. Roberts: A theory of dimension.
-Theory, 11 (1997), 103-159. MR 1444286 (98i:46065)
- 9.
- C. Pinzari, J.E. Roberts: A duality theorem for ergodic actions of compact quantum groups on
-algebras. Comm. Math. Phys., 277 (2008), 385-421. MR 2358289 (2008k:46203)
- 10.
- C. Pinzari, J.E. Roberts: Ergodic actions of
on -algebras from subfactors. J. Geom. Phys., 60 (2010), 403-416. MR 2600003 (2011f:46084)
- 11.
- C. Pinzari, J.E. Roberts: A theory of induction and classification of tensor
-categories, J. Noncomm. Geom., to appear, arXiv:0907.2459.
- 12.
- S. Vaes, R. Vergnioux: The boundary of universal discrete quantum groups, exactness, and factoriality. Duke Math. J., 140 (2007), 35-84. MR 2355067 (2010a:46166)
- 13.
- S. Wang: Ergodic actions of universal quantum groups on operator algebras. Comm. Math. Phys., 203 (1999), 481-498. MR 1697607 (2000j:46128)
- 14.
- A. Wassermann: Ergodic actions of compact groups on operator algebras. III. Classification for
. Invent. Math., 93 (1988), 309-354. MR 948104 (91e:46093)
- 15.
- S.L. Woronowicz: Compact matrix pseudogroups. Comm. Math. Phys., 111 (1987), 613-665. MR 901157 (88m:46079)
- 16.
- S.L. Woronowicz: Compact quantum groups. In: Symétries quantiques (Les Houches, 1995), 845-884, North-Holland, Amsterdam, 1998. MR 1616348 (99m:46164)
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Additional Information
Claudia Pinzari
Affiliation:
Dipartimento di Matematica, Sapienza Università di Roma, 00185–Roma, Italy
Email:
pinzari@mat.uniroma1.it
DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11482-0
PII:
S 0002-9939(2012)11482-0
Received by editor(s):
February 15, 2011
Received by editor(s) in revised form:
July 14, 2011
Posted:
July 5, 2012
Dedicated:
Dedicated to the memory of Claudio D’Antoni
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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