Measurable Kac cohomology for bicrossed products

Saad Baaj (1) , Georges Skandalis (2) , Stefaan Vaes (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 IMJ - Institut de Mathématiques de Jussieu

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 topological 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.

Domaines: Algèbres d'opérateurs [math.OA]; Algèbres quantiques [math.QA]

Saad Baaj, Georges Skandalis, Stefaan Vaes. Measurable Kac cohomology for bicrossed products. Transactions of the American Mathematical Society, 2005, 357, pp.1497-1524. ⟨hal-00012255⟩