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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Measurable Kac cohomology for bicrossed products


Authors: Saad Baaj, Georges Skandalis and Stefaan Vaes
Journal: Trans. Amer. Math. Soc. 357 (2005), 1497-1524
MSC (2000): Primary 22D05; Secondary 55N99, 20J06
Published electronically: November 23, 2004
MathSciNet review: 2115374
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Abstract: We study the Kac cohomology for matched pairs of locally compact groups. This cohomology theory arises from the extension theory of locally compact quantum groups. We prove a measurable version of the Kac exact sequence and provide methods to compute the cohomology. We give explicit calculations in several examples using results of Moore and Wigner.


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Additional Information

Saad Baaj
Affiliation: Laboratoire de Mathématiques Pures, Université Blaise Pascal, Bâtiment de Mathématiques, F–63177 Aubière Cedex, France
Email: Saad.Baaj@math.univ-bpclermont.fr

Georges Skandalis
Affiliation: Algèbres d’Opérateurs et Représentations, Institut de Mathématiques de Jussieu, 175, rue du Chevaleret, F–75013 Paris, France
Email: skandal@math.jussieu.fr

Stefaan Vaes
Affiliation: Algèbres d’Opérateurs et Représentations, Institut de Mathématiques de Jussieu, 175, rue du Chevaleret, F–75013 Paris, France – and – Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Email: vaes@math.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03734-1
PII: S 0002-9947(04)03734-1
Keywords: Measurable cohomology, locally compact quantum groups, extensions, Kac exact sequence
Received by editor(s): October 24, 2003
Published electronically: November 23, 2004
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.