Letters in Mathematical Physics

, Volume 1, Issue 1, pp 83–91 | Cite as

On the 1-cohomology of Lie groups

  • Georges Pinczon
  • Jacques Simon


Given a continous representation of a Lie group in a Banach space we study its 1-cohomology. We prove that the computation of the 1-cocycles can be reduced to that of the 1-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.


Statistical Physic Banach Space Finite Number Group Theory Irreducible Representation 
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Copyright information

© D. Reidel Publishing Company 1975

Authors and Affiliations

  • Georges Pinczon
    • 1
  • Jacques Simon
    • 1
  1. 1.Laboratoire de Physique Mathématique, Faculté des Sciences MirandeUniversité de DijonDIJONFrance

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