Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Compact quantum groups associated with monoidal functors

Author(s): Huu Hung Bui
Journal: Proc. Amer. Math. Soc. 126 (1998), 1081-1088.
MSC (1991): Primary 46L89, 46M15, 18E10
MathSciNet review: 1422851
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We provide a ${C}^\ast$-algebra structure on the bialgebra associated with a monoidal linear ${}^\ast$-functor. The ${C}^\ast$-algebra obtained in this way is a compact quantum group in the sense of Baaj and Skandalis. We show that the category of finite dimensional unitary corepresentations of this ${C}^\ast$-algebra is equivalent to the given category.

References:

[B]
H. H. Bui, Compact quantum groups and their corepresentations, Bull. Austral. Math. Soc., to appear.

[B2]
H. H. Bui, Morita equivalence of twisted crossed products by coactions, J. Funct. Anal. 123 (1994), 59-98. MR 95g:46121

[BS]
S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualite pour les produits crossés de $C^{*}$-algèbres, Ann. Sci. Ec. Norm. Sup. 26 (1993), 425-488. MR 94e:46127

[D]
P. Deligne, Catégories Tannakiennes, The Grothendieck Festschrift, Progress in Math. 87, Birkhäuser, 1990, pp. 111-195. MR 92d:14002

[DR]
S. Doplicher and J. E. Roberts, A new duality theory for compact groups, Invent. Math. 98 (1989), 157-218. MR 90k:22005

[JS]
A. Joyal and R. Street, An introduction to Tannaka duality and quantum groups, Lecture Notes in Mathematics, Vol. 1488, Springer-Verlag, New York, 1991, pp. 413-492. MR 93f:18015

[JS2]
A. Joyal and R. Street, Braided tensor categories, Adv. Math. 102 (1993), 20-78. MR 94m:18008

[K]
C. Kassel, Quantum groups, Graduate Texts in Mathematics, Vol. 155, Springer-Verlag, New York, 1995. MR 96e:17041

[KT]
C. Kassel and V. Turaev, Double construction for monoidal categories, Acta Math. 175 (1995), 1-48. MR 96m:18015

[Sc]
P. Schauenburg, Tannaka duality for arbitrary Hopf algebras, Algebra-Berichte Vol. 66, Verlag Reinhard Fisher Munchen, 1992.

[Sk]
G. Skandalis, Operator algebras and Duality,, Proceedings of the International Congress of Mathematicians, vol. 2, 1990, pp. 997-1009. MR 93d:46094

[W]
S. L. Woronowicz, Compact matrix pseudogroups, Commun. Math. Phys. 111 (1987), 613-665. MR 88m:46079

[W2]
S. L. Woronowicz, Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93 (1988), 35-76. MR 90e:22033

[Y]
D. N. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Cambridge Philos. Soc. 108 (1990), 261-290. MR 91k:16028

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L89, 46M15, 18E10

Retrieve articles in all Journals with MSC (1991): 46L89, 46M15, 18E10

Additional Information:

Huu Hung Bui
Affiliation: Department of Mathematics, Macquarie University, New South Wales 2109, Australia
Address at time of publication: School of Mathematics, The University of New South Wales, Sydney, New South Wales 2052, Australia
Email: hung@alpha.maths.unsw.edu.au

DOI: 10.1090/S0002-9939-98-04094-5
PII: S 0002-9939(98)04094-5
Received by editor(s): August 7, 1996
Received by editor(s) in revised form: September 23, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia