On the Third-Degree Continuous Cohomology of Simple Lie Groups

JOURNAL OF LIE THEORY（2019）

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摘要

We show that the collection of connected, simple Lie groups that have non-vani-shing third-degree continuous cohomology with trivial R -coefficients consists precisely of all simple complex Lie groups and of <(SL2(R))over tilde>.

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关键词

Continuous cohomology,simple Lie groups,complex structures,Lie algebra cohomology,van Est's theorem,cohomology of homogeneous spaces of simple Lie groups,Dynkin index

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