Journal of Lie Theory

no. 4
On The Third-Degree Continuous Cohomology of Simple Lie Groups
Journal of Lie Theory, Volume 29 (2019) no. 4, pp. 1007-1016
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 $\widetilde{{\rm SL}_2(\mathbb{R})}$.
DOI: 10.5802/jolt.1089
Classification: 22E41, 22E46, 57T10, 57T15
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 
@article{JOLT_2019_29_4_a6,
     author = {C. De la Cruz Mengual},
     title = {On {The} {Third-Degree} {Continuous} {Cohomology} of {Simple} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {1007--1016},
     year = {2019},
     volume = {29},
     number = {4},
     doi = {10.5802/jolt.1089},
     zbl = {1440.22025},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1089/}
}
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%J Journal of Lie Theory
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C. De la Cruz Mengual. On The Third-Degree Continuous Cohomology of Simple Lie Groups. Journal of Lie Theory, Volume 29 (2019) no. 4, pp. 1007-1016. doi: 10.5802/jolt.1089

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