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Measurable Kac cohomology for bicrossed products |
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| Authors: | Saad Baaj Georges Skandalis Stefaan Vaes |
| Affiliation: | Laboratoire de Mathématiques Pures, Université Blaise Pascal, Bâtiment de Mathématiques, F--63177 Aubière Cedex, France ; Algèbres d'Opérateurs et Représentations, Institut de Mathématiques de Jussieu, 175, rue du Chevaleret, F--75013 Paris, France ; 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 |
| 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. |
| Keywords: | Measurable cohomology locally compact quantum groups extensions Kac exact sequence |
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