Vol. 39, No. 2, 1971

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Cohomology of group germs and Lie algebras

Stanisław Sławomir Świerczkowski

Vol. 39 (1971), No. 2, 471–482
Abstract

Let π be a continuous representation of a Lie group G in a finite dimensional real vector space V . Denote by H(G,V ) the cohomology with empty supports in the sense of Sze-tsen Hu. If L is the Lie algebra of G,π induces an L-module structure on V and there is the associated cohomology H(L,V ) of Chevalley-Eilenberg. Our main result is the construction of an isomorphism H(G,V ) H(L,V ).

Mathematical Subject Classification 2000
Primary: 18H25
Secondary: 22E05, 57F10
Milestones
Received: 3 February 1970
Published: 1 November 1971
Authors
Stanisław Sławomir Świerczkowski