Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 29 (2019), No. 4, 1007--1016Copyright Heldermann Verlag 2019 On The Third-Degree Continuous Cohomology of Simple Lie Groups Carlos De la Cruz Mengual Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zurich, Switzerland carlos.delacruz@math.ethz.ch [Abstract-pdf] We show that the collection of connected, simple Lie groups that have non-vani\-shing third-degree continuous cohomology with trivial $\mathbb{R}$-coefficients consists precisely of all simple complex Lie groups and of $\widetilde{{\rm SL}_2(\mathbb{R})}$. Keywords: Continuous cohomology, simple Lie groups, complex structures, Lie algebra cohomology, van Est's theorem, cohomology of homogeneous spaces of simple Lie groups, Dynkin index. MSC: 22E41, 22E46, 57T10, 57T15. [ Fulltext-pdf  (128  KB)] for subscribers only.