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Journal of Lie Theory 29 (2019), No. 4, 1007--1016
Copyright 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


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.

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