Low-order cohomology of semi-simple Lie groups with applications to continuous tensor products and current groups
The paper gives a survey of first and second-order continuous cohomology of groups in view of possible applications. In particular the standard construction for so-called ''factorizable representations of current groups'' is given and concretely realized for the current group of \(SU(1;1)\). The probabilistic aspect of the theory is, however, only briefly mentioned in the paper. The second named author has in the meantime obtained an analogue of the Lévy-Khintchin formula (in terms of cohomology groups) for the classical split rank one groups. Moreover interesting connections of the theory to Furstenberg's work on noncommuting random products and Gangolli's work on Lévy-Schoenberg kernels have come to light. Thus, apart from applications in mathematical physics, continuous cohomology groups also play an important part in abstract probability theory.
scientific article; zbMATH DE number 3844035
scientific article