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On the 1-cohomology of Lie groups

✍ Scribed by Georges Pinczon; Jacques Simon

Publisher
Springer
Year
1975
Tongue
English
Weight
464 KB
Volume
1
Category
Article
ISSN
0377-9017

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✦ Synopsis

Given a continuous representation of a Lie group in a Banach space we study its l-cohomology. We prove that the computation of the l-cocycles can be reduced to that of the l-cocycles of the differential of the representation. When the group is semi-simple and the representation is K-finite, we prove that the cohomology is equivalent to the cohomology of the Lie algebra representation on K-finite vectors. We prove, using Casimir operators, that there exist only a finite number of irreducible representation of a semi-simple Lie group with a non-trivial cohomology. Exemples of such representations are given.

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