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
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.
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