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Letters in Mathematical Physics

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

On the 1-cohomology of Lie groups

  • Georges Pinczon
  • Jacques Simon
Article

Abstract

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.

Keywords

Statistical Physic Banach Space Finite Number Group Theory Irreducible Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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