
Journal of Lie Theory 29 (2019), No. 4, 10071016 Copyright Heldermann Verlag 2019 On The ThirdDegree 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 [Abstractpdf] We show that the collection of connected, simple Lie groups that have nonvani\shing thirddegree 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. [ Fulltextpdf (128 KB)] for subscribers only. 