Cohomology of group germs and Lie algebras

Stanisław Sławomir Świerczkowski

Vol. 39 (1971), No. 2, 471–482

DOI: 10.2140/pjm.1971.39.471

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