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Compact quantum group actions on C*-algebras and invariant derivations
Author(s):
Raluca
Dumitru;
Costel
Peligrad
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3977-3984.
MSC (2000):
Primary 46L57, 20G42;
Secondary 81T99
Posted:
July 27, 2007
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Abstract:
We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.
References:
-
- 1.
- S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de
 -algèbres, Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 4, 425-488, MR1235438 (94e:46127). MR 1235438 (94e:46127) - 2.
- J. Bichon, A. de Rijdt, S. Vaes, Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups, Commun. Math. Phys., to appear. MR 2202309 (2007a:46072)
- 3.
- F. Boca, Ergodic actions of compact matrix pseudogroups on
 -algebras, Recent advances in operator algebras (Orléans, 1992), Astérisque No. 232, (1995), 93-109, MR1372527 (97d:46075). MR 1372527 (97d:46075) - 4.
- O. Bratteli and D. Robinson, Operator algebras and quantum statistical mechanics. I, Springer-Verlag, New York-Heidelberg-Berlin (1979). MR 611508 (82k:82013)
- 5.
- O. Bratteli, Derivations, dissipations and group actions on C*-algebras, Springer-Verlag Lecture notes Nr.1229 (1986). MR 871870 (88e:46050)
- 6.
- F. Goodman and P. E. T. Jørgensen, Unbounded derivations commuting with compact group actions, Comm. Math. Phys. 82 (1981/82), no. 3, 399-405, MR0641770 (83b:46083). MR 641770 (83b:46083)
- 7.
- C. Peligrad, Derivations of C*-algebras that are invariant under an automorphism group, In Operator Theory: Adv. Appl. 6 Birkhäuser, Basel-Boston, 181-193 (1982). MR 685463 (84g:46100b)
- 8.
- P. Podles, Symmetries of quantum spaces. Subgroups and quotient spaces of quantum
 and  groups, Comm. Math. Phys. 170 (1995), no. 1, 1-20, MR1331688 (96j:58013). MR 1331688 (96j:58013) - 9.
- S. Sakai, On one-parameter groups of
 -automorphisms on operator algebras and the corresponding unbounded derivations, Amer. J. Math. 98 (1976), 427-440 MR 0412824 (54:945) - 10.
- S. Wang, Ergodic actions of universal quantum groups on operator algebras, Comm. Math. Phys. 203 (1999), no. 2, 481-498, MR1697607 (2000j:46128). MR 1697607 (2000j:46128)
- 11.
- S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613-665, MR0901157 (88m:46079). MR 901157 (88m:46079)
- 12.
- S. L. Woronowicz, Compact quantum groups, Quantum Symmetries, Proceedings of the Les Houches summer school (1995), North Holland, Amsterdam (1998), 845-884. MR 1616348 (99m:46164)
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Additional Information:
Raluca
Dumitru
Affiliation:
Department of Mathematics, University of Cincinnati, Cincinnati, Ohio; and Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Email:
dumitrra@email.uc.edu
Costel
Peligrad
Affiliation:
Department of Mathematics, University of Cincinnati, Cincinnati, Ohio; and Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Email:
costel.peligrad@UC.Edu
DOI:
10.1090/S0002-9939-07-09011-9
PII:
S 0002-9939(07)09011-9
Received by editor(s):
March 8, 2006
Received by editor(s) in revised form:
November 25, 2006
Posted:
July 27, 2007
Additional Notes:
This research was supported by the Taft Foundation. The first author was supported by a Taft Advanced Graduate Fellowship and by a Taft Graduate Enrichment Award. The second author was supported by a Taft Research Travel Grant.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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